Class UnivariateDiscreteDistribution

Abstract class for univariate discrete probability distributions.
Inheritance
System.Object
DistributionBase
UnivariateDiscreteDistribution
UniformDiscreteDistribution
Implements
System.IFormattable
System.ICloneable
Mars.Common.Core.Random.IRandomNumberGenerator<System.Double>
Mars.Common.Core.Random.IRandomNumberGenerator<System.Int32>
Inherited Members
System.Object.Equals(System.Object)
System.Object.Equals(System.Object, System.Object)
System.Object.GetHashCode()
System.Object.GetType()
System.Object.MemberwiseClone()
System.Object.ReferenceEquals(System.Object, System.Object)
Namespace: Mars.Numerics.Statistics.Base
Assembly: Mars.Numerics.dll
Syntax
[Serializable]
public abstract class UnivariateDiscreteDistribution : DistributionBase, IFormattable, IUnivariateDistribution<int>, IUnivariateDistribution, IDistribution, ICloneable, IUnivariateDistribution<double>, ISampleableDistribution<double>, IRandomNumberGenerator<double>, ISampleableDistribution<int>, IRandomNumberGenerator<int>
Remarks

A probability distribution identifies either the probability of each value of an unidentified random variable (when the variable is discrete), or the probability of the value falling within a particular interval (when the variable is continuous).

The probability distribution describes the range of possible values that a random variable can attain and the probability that the value of the random variable is within any (measurable) subset of that range.

The function describing the probability that a given discrete value will occur is called the probability function (or probability mass function, abbreviated PMF), and the function describing the cumulative probability that a given value or any value smaller than it will occur is called the distribution function (or cumulative distribution function, abbreviated CDF).

References:

Properties

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Entropy

Gets the entropy for this distribution.
Declaration
public abstract double Entropy { get; }
Property Value
Type Description
System.Double The distribution's entropy.
Remarks

A probability distribution identifies either the probability of each value of an unidentified random variable (when the variable is discrete), or the probability of the value falling within a particular interval (when the variable is continuous).

The probability distribution describes the range of possible values that a random variable can attain and the probability that the value of the random variable is within any (measurable) subset of that range.

The function describing the probability that a given discrete value will occur is called the probability function (or probability mass function, abbreviated PMF), and the function describing the cumulative probability that a given value or any value smaller than it will occur is called the distribution function (or cumulative distribution function, abbreviated CDF).

References:

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Mean

Gets the mean for this distribution.
Declaration
public abstract double Mean { get; }
Property Value
Type Description
System.Double The distribution's mean value.
Remarks

A probability distribution identifies either the probability of each value of an unidentified random variable (when the variable is discrete), or the probability of the value falling within a particular interval (when the variable is continuous).

The probability distribution describes the range of possible values that a random variable can attain and the probability that the value of the random variable is within any (measurable) subset of that range.

The function describing the probability that a given discrete value will occur is called the probability function (or probability mass function, abbreviated PMF), and the function describing the cumulative probability that a given value or any value smaller than it will occur is called the distribution function (or cumulative distribution function, abbreviated CDF).

References:

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Median

Gets the median for this distribution.
Declaration
public virtual double Median { get; }
Property Value
Type Description
System.Double The distribution's median value.
Remarks

A probability distribution identifies either the probability of each value of an unidentified random variable (when the variable is discrete), or the probability of the value falling within a particular interval (when the variable is continuous).

The probability distribution describes the range of possible values that a random variable can attain and the probability that the value of the random variable is within any (measurable) subset of that range.

The function describing the probability that a given discrete value will occur is called the probability function (or probability mass function, abbreviated PMF), and the function describing the cumulative probability that a given value or any value smaller than it will occur is called the distribution function (or cumulative distribution function, abbreviated CDF).

References:

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Mode

Gets the mode for this distribution.
Declaration
public virtual double Mode { get; }
Property Value
Type Description
System.Double The distribution's mode value.
Remarks

A probability distribution identifies either the probability of each value of an unidentified random variable (when the variable is discrete), or the probability of the value falling within a particular interval (when the variable is continuous).

The probability distribution describes the range of possible values that a random variable can attain and the probability that the value of the random variable is within any (measurable) subset of that range.

The function describing the probability that a given discrete value will occur is called the probability function (or probability mass function, abbreviated PMF), and the function describing the cumulative probability that a given value or any value smaller than it will occur is called the distribution function (or cumulative distribution function, abbreviated CDF).

References:

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Quartiles

Gets the Quartiles for this distribution.
Declaration
public virtual DoubleRange Quartiles { get; }
Property Value
Type Description
DoubleRange A DoubleRange object containing the first quartile (Q1) as its minimum value, and the third quartile (Q2) as the maximum.
Remarks

A probability distribution identifies either the probability of each value of an unidentified random variable (when the variable is discrete), or the probability of the value falling within a particular interval (when the variable is continuous).

The probability distribution describes the range of possible values that a random variable can attain and the probability that the value of the random variable is within any (measurable) subset of that range.

The function describing the probability that a given discrete value will occur is called the probability function (or probability mass function, abbreviated PMF), and the function describing the cumulative probability that a given value or any value smaller than it will occur is called the distribution function (or cumulative distribution function, abbreviated CDF).

References:

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Support

Gets the support interval for this distribution.
Declaration
public abstract IntRange Support { get; }
Property Value
Type Description
IntRange A IntRange containing the support interval for this distribution.
Remarks

A probability distribution identifies either the probability of each value of an unidentified random variable (when the variable is discrete), or the probability of the value falling within a particular interval (when the variable is continuous).

The probability distribution describes the range of possible values that a random variable can attain and the probability that the value of the random variable is within any (measurable) subset of that range.

The function describing the probability that a given discrete value will occur is called the probability function (or probability mass function, abbreviated PMF), and the function describing the cumulative probability that a given value or any value smaller than it will occur is called the distribution function (or cumulative distribution function, abbreviated CDF).

References:

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Variance

Gets the variance for this distribution.
Declaration
public abstract double Variance { get; }
Property Value
Type Description
System.Double The distribution's variance.
Remarks

A probability distribution identifies either the probability of each value of an unidentified random variable (when the variable is discrete), or the probability of the value falling within a particular interval (when the variable is continuous).

The probability distribution describes the range of possible values that a random variable can attain and the probability that the value of the random variable is within any (measurable) subset of that range.

The function describing the probability that a given discrete value will occur is called the probability function (or probability mass function, abbreviated PMF), and the function describing the cumulative probability that a given value or any value smaller than it will occur is called the distribution function (or cumulative distribution function, abbreviated CDF).

References:

Methods

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BaseDistributionFunction(Int32)

Computes the cumulative distribution function by summing the outputs of the ProbabilityMassFunction(Int32) for all elements in the distribution domain. Note that this method should not be used in case there is a more efficient formula for computing the CDF of a distribution.
Declaration
protected double BaseDistributionFunction(int k)
Parameters
Type Name Description
System.Int32 k A single point in the distribution range.
Returns
Type Description
System.Double
Remarks

A probability distribution identifies either the probability of each value of an unidentified random variable (when the variable is discrete), or the probability of the value falling within a particular interval (when the variable is continuous).

The probability distribution describes the range of possible values that a random variable can attain and the probability that the value of the random variable is within any (measurable) subset of that range.

The function describing the probability that a given discrete value will occur is called the probability function (or probability mass function, abbreviated PMF), and the function describing the cumulative probability that a given value or any value smaller than it will occur is called the distribution function (or cumulative distribution function, abbreviated CDF).

References:

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BaseInverseDistributionFunction(Double)

Gets the inverse of the cumulative distribution function (icdf) for this distribution evaluated at probability p using a numerical approximation based on binary search.
Declaration
protected int BaseInverseDistributionFunction(double p)
Parameters
Type Name Description
System.Double p A probability value between 0 and 1.
Returns
Type Description
System.Int32 A sample which could original the given probability value when applied in the DistributionFunction(Int32).
Remarks
The Inverse Cumulative Distribution Function (ICDF) specifies, for a given probability, the value which the random variable will be at, or below, with that probability.
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ComplementaryDistributionFunction(Int32, Boolean)

Gets the complementary cumulative distribution function (ccdf) for this distribution evaluated at point k. This function is also known as the Survival function.
Declaration
public double ComplementaryDistributionFunction(int k, bool inclusive)
Parameters
Type Name Description
System.Int32 k A single point in the distribution range.
System.Boolean inclusive True to return P(X >= x), false to return P(X > x). Default is false.
Returns
Type Description
System.Double
Remarks
The Complementary Cumulative Distribution Function (CCDF) is the complement of the Cumulative Distribution Function, or 1 minus the CDF.
Examples
// Compute P(X = k) 
double equal = dist.ProbabilityMassFunction(k: 1);

// Compute P(X < k) 
double less = dist.DistributionFunction(k: 1, inclusive: false);

// Compute P(X ≤ k) 
double lessThanOrEqual = dist.DistributionFunction(k: 1, inclusive: true);

// Compute P(X > k) 
double greater = dist.ComplementaryDistributionFunction(k: 1);

// Compute P(X ≥ k) 
double greaterThanOrEqual = dist.ComplementaryDistributionFunction(k: 1, inclusive: true);
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ComplementaryDistributionFunction(Int32)

Gets P(X > k) the complementary cumulative distribution function (ccdf) for this distribution evaluated at point k. This function is also known as the Survival function.
Declaration
public double ComplementaryDistributionFunction(int k)
Parameters
Type Name Description
System.Int32 k A single point in the distribution range.
Returns
Type Description
System.Double
Remarks
The Complementary Cumulative Distribution Function (CCDF) is the complement of the Cumulative Distribution Function, or 1 minus the CDF.
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CumulativeHazardFunction(Int32)

Gets the cumulative hazard function for this distribution evaluated at point x.
Declaration
public virtual double CumulativeHazardFunction(int x)
Parameters
Type Name Description
System.Int32 x A single point in the distribution range.
Returns
Type Description
System.Double The cumulative hazard function H(x) evaluated at x in the current distribution.
Remarks

A probability distribution identifies either the probability of each value of an unidentified random variable (when the variable is discrete), or the probability of the value falling within a particular interval (when the variable is continuous).

The probability distribution describes the range of possible values that a random variable can attain and the probability that the value of the random variable is within any (measurable) subset of that range.

The function describing the probability that a given discrete value will occur is called the probability function (or probability mass function, abbreviated PMF), and the function describing the cumulative probability that a given value or any value smaller than it will occur is called the distribution function (or cumulative distribution function, abbreviated CDF).

References:

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DistributionFunction(Double[])

Abstract class for univariate discrete probability distributions.
Declaration
public double DistributionFunction(double[] x)
Parameters
Type Name Description
System.Double[] x
Returns
Type Description
System.Double
Remarks

A probability distribution identifies either the probability of each value of an unidentified random variable (when the variable is discrete), or the probability of the value falling within a particular interval (when the variable is continuous).

The probability distribution describes the range of possible values that a random variable can attain and the probability that the value of the random variable is within any (measurable) subset of that range.

The function describing the probability that a given discrete value will occur is called the probability function (or probability mass function, abbreviated PMF), and the function describing the cumulative probability that a given value or any value smaller than it will occur is called the distribution function (or cumulative distribution function, abbreviated CDF).

References:

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DistributionFunction(Int32, Boolean)

Gets P(X ≤ k) or P(X < k), the cumulative distribution function (cdf) for this distribution evaluated at point k, depending on the value of the inclusive parameter.
Declaration
public double DistributionFunction(int k, bool inclusive)
Parameters
Type Name Description
System.Int32 k A single point in the distribution range.
System.Boolean inclusive True to return P(X ≤ x), false to return P(X < x). Default is true.
Returns
Type Description
System.Double
Remarks
The Cumulative Distribution Function (CDF) describes the cumulative probability that a given value or any value smaller than it will occur.
Examples
// Compute P(X = k) 
double equal = dist.ProbabilityMassFunction(k: 1);

// Compute P(X < k) 
double less = dist.DistributionFunction(k: 1, inclusive: false);

// Compute P(X ≤ k) 
double lessThanOrEqual = dist.DistributionFunction(k: 1, inclusive: true);

// Compute P(X > k) 
double greater = dist.ComplementaryDistributionFunction(k: 1);

// Compute P(X ≥ k) 
double greaterThanOrEqual = dist.ComplementaryDistributionFunction(k: 1, inclusive: true);
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DistributionFunction(Int32, Int32)

Gets the cumulative distribution function (cdf) for this distribution in the semi-closed interval (a; b] given as P(a < X ≤ b).
Declaration
public double DistributionFunction(int a, int b)
Parameters
Type Name Description
System.Int32 a The start of the semi-closed interval (a; b].
System.Int32 b The end of the semi-closed interval (a; b].
Returns
Type Description
System.Double
Remarks
The Cumulative Distribution Function (CDF) describes the cumulative probability that a given value or any value smaller than it will occur.
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DistributionFunction(Int32)

Gets P(X ≤ k), the cumulative distribution function (cdf) for this distribution evaluated at point k.
Declaration
public double DistributionFunction(int k)
Parameters
Type Name Description
System.Int32 k A single point in the distribution range.
Returns
Type Description
System.Double
Remarks
The Cumulative Distribution Function (CDF) describes the cumulative probability that a given value or any value smaller than it will occur.
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Generate()

Generates a random observation from the current distribution.
Declaration
public int Generate()
Returns
Type Description
System.Int32 A random observations drawn from this distribution.
Remarks

A probability distribution identifies either the probability of each value of an unidentified random variable (when the variable is discrete), or the probability of the value falling within a particular interval (when the variable is continuous).

The probability distribution describes the range of possible values that a random variable can attain and the probability that the value of the random variable is within any (measurable) subset of that range.

The function describing the probability that a given discrete value will occur is called the probability function (or probability mass function, abbreviated PMF), and the function describing the cumulative probability that a given value or any value smaller than it will occur is called the distribution function (or cumulative distribution function, abbreviated CDF).

References:

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Generate(FastRandom)

Generates a random observation from the current distribution.
Declaration
public virtual int Generate(FastRandom source)
Parameters
Type Name Description
Mars.Common.Core.Random.FastRandom source The random number generator to use as a source of randomness. Default is to use System.Random.
Returns
Type Description
System.Int32 A random observations drawn from this distribution.
Remarks

A probability distribution identifies either the probability of each value of an unidentified random variable (when the variable is discrete), or the probability of the value falling within a particular interval (when the variable is continuous).

The probability distribution describes the range of possible values that a random variable can attain and the probability that the value of the random variable is within any (measurable) subset of that range.

The function describing the probability that a given discrete value will occur is called the probability function (or probability mass function, abbreviated PMF), and the function describing the cumulative probability that a given value or any value smaller than it will occur is called the distribution function (or cumulative distribution function, abbreviated CDF).

References:

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Generate(Int32, FastRandom)

Generates a random vector of observations from the current distribution.
Declaration
public int[] Generate(int samples, FastRandom source)
Parameters
Type Name Description
System.Int32 samples The number of samples to generate.
Mars.Common.Core.Random.FastRandom source The random number generator to use as a source of randomness. Default is to use System.Random.
Returns
Type Description
System.Int32[] A random vector of observations drawn from this distribution.
Remarks

A probability distribution identifies either the probability of each value of an unidentified random variable (when the variable is discrete), or the probability of the value falling within a particular interval (when the variable is continuous).

The probability distribution describes the range of possible values that a random variable can attain and the probability that the value of the random variable is within any (measurable) subset of that range.

The function describing the probability that a given discrete value will occur is called the probability function (or probability mass function, abbreviated PMF), and the function describing the cumulative probability that a given value or any value smaller than it will occur is called the distribution function (or cumulative distribution function, abbreviated CDF).

References:

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Generate(Int32, Double[], FastRandom)

Generates a random vector of observations from the current distribution.
Declaration
public virtual double[] Generate(int samples, double[] result, FastRandom source)
Parameters
Type Name Description
System.Int32 samples The number of samples to generate.
System.Double[] result The location where to store the samples.
Mars.Common.Core.Random.FastRandom source The random number generator to use as a source of randomness. Default is to use System.Random.
Returns
Type Description
System.Double[] A random vector of observations drawn from this distribution.
Remarks

A probability distribution identifies either the probability of each value of an unidentified random variable (when the variable is discrete), or the probability of the value falling within a particular interval (when the variable is continuous).

The probability distribution describes the range of possible values that a random variable can attain and the probability that the value of the random variable is within any (measurable) subset of that range.

The function describing the probability that a given discrete value will occur is called the probability function (or probability mass function, abbreviated PMF), and the function describing the cumulative probability that a given value or any value smaller than it will occur is called the distribution function (or cumulative distribution function, abbreviated CDF).

References:

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Generate(Int32, Double[])

Generates a random vector of observations from the current distribution.
Declaration
public double[] Generate(int samples, double[] result)
Parameters
Type Name Description
System.Int32 samples The number of samples to generate.
System.Double[] result The location where to store the samples.
Returns
Type Description
System.Double[] A random vector of observations drawn from this distribution.
Remarks

A probability distribution identifies either the probability of each value of an unidentified random variable (when the variable is discrete), or the probability of the value falling within a particular interval (when the variable is continuous).

The probability distribution describes the range of possible values that a random variable can attain and the probability that the value of the random variable is within any (measurable) subset of that range.

The function describing the probability that a given discrete value will occur is called the probability function (or probability mass function, abbreviated PMF), and the function describing the cumulative probability that a given value or any value smaller than it will occur is called the distribution function (or cumulative distribution function, abbreviated CDF).

References:

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Generate(Int32, Int32[], FastRandom)

Generates a random vector of observations from the current distribution.
Declaration
public virtual int[] Generate(int samples, int[] result, FastRandom source)
Parameters
Type Name Description
System.Int32 samples The number of samples to generate.
System.Int32[] result The location where to store the samples.
Mars.Common.Core.Random.FastRandom source The random number generator to use as a source of randomness. Default is to use System.Random.
Returns
Type Description
System.Int32[] A random vector of observations drawn from this distribution.
Remarks

A probability distribution identifies either the probability of each value of an unidentified random variable (when the variable is discrete), or the probability of the value falling within a particular interval (when the variable is continuous).

The probability distribution describes the range of possible values that a random variable can attain and the probability that the value of the random variable is within any (measurable) subset of that range.

The function describing the probability that a given discrete value will occur is called the probability function (or probability mass function, abbreviated PMF), and the function describing the cumulative probability that a given value or any value smaller than it will occur is called the distribution function (or cumulative distribution function, abbreviated CDF).

References:

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Generate(Int32, Int32[])

Generates a random vector of observations from the current distribution.
Declaration
public int[] Generate(int samples, int[] result)
Parameters
Type Name Description
System.Int32 samples The number of samples to generate.
System.Int32[] result The location where to store the samples.
Returns
Type Description
System.Int32[] A random vector of observations drawn from this distribution.
Remarks

A probability distribution identifies either the probability of each value of an unidentified random variable (when the variable is discrete), or the probability of the value falling within a particular interval (when the variable is continuous).

The probability distribution describes the range of possible values that a random variable can attain and the probability that the value of the random variable is within any (measurable) subset of that range.

The function describing the probability that a given discrete value will occur is called the probability function (or probability mass function, abbreviated PMF), and the function describing the cumulative probability that a given value or any value smaller than it will occur is called the distribution function (or cumulative distribution function, abbreviated CDF).

References:

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Generate(Int32)

Generates a random vector of observations from the current distribution.
Declaration
public int[] Generate(int samples)
Parameters
Type Name Description
System.Int32 samples The number of samples to generate.
Returns
Type Description
System.Int32[] A random vector of observations drawn from this distribution.
Remarks

A probability distribution identifies either the probability of each value of an unidentified random variable (when the variable is discrete), or the probability of the value falling within a particular interval (when the variable is continuous).

The probability distribution describes the range of possible values that a random variable can attain and the probability that the value of the random variable is within any (measurable) subset of that range.

The function describing the probability that a given discrete value will occur is called the probability function (or probability mass function, abbreviated PMF), and the function describing the cumulative probability that a given value or any value smaller than it will occur is called the distribution function (or cumulative distribution function, abbreviated CDF).

References:

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GetRange(Double)

Gets the distribution range within a given percentile.
Declaration
public virtual IntRange GetRange(double percentile)
Parameters
Type Name Description
System.Double percentile The percentile at which the distribution ranges will be returned.
Returns
Type Description
IntRange A DoubleRange object containing the minimum value for the distribution value, and the third quartile (Q2) as the maximum.
Remarks
If 0.25 is passed as the percentile argument, this function returns the same as the Quartiles function.
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HazardFunction(Int32)

Gets the hazard function, also known as the failure rate or the conditional failure density function for this distribution evaluated at point x.
Declaration
public virtual double HazardFunction(int x)
Parameters
Type Name Description
System.Int32 x A single point in the distribution range.
Returns
Type Description
System.Double The conditional failure density function h(x) evaluated at x in the current distribution.
Remarks
The hazard function is the ratio of the probability density function f(x) to the survival function, S(x).
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InnerComplementaryDistributionFunction(Int32)

Gets P(X > k) the complementary cumulative distribution function (ccdf) for this distribution evaluated at point k. This function is also known as the Survival function.
Declaration
protected virtual double InnerComplementaryDistributionFunction(int k)
Parameters
Type Name Description
System.Int32 k A single point in the distribution range.
Returns
Type Description
System.Double
Remarks
The Complementary Cumulative Distribution Function (CCDF) is the complement of the Cumulative Distribution Function, or 1 minus the CDF.
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InnerDistributionFunction(Int32)

Gets P(X ≤ k), the cumulative distribution function (cdf) for this distribution evaluated at point k.
Declaration
protected abstract double InnerDistributionFunction(int k)
Parameters
Type Name Description
System.Int32 k A single point in the distribution range.
Returns
Type Description
System.Double
Remarks
The Cumulative Distribution Function (CDF) describes the cumulative probability that a given value or any value smaller than it will occur.
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InnerInverseDistributionFunction(Double)

Gets the inverse of the cumulative distribution function (icdf) for this distribution evaluated at probability p. This function is also known as the Quantile function.
Declaration
protected virtual int InnerInverseDistributionFunction(double p)
Parameters
Type Name Description
System.Double p A probability value between 0 and 1.
Returns
Type Description
System.Int32 A sample which could original the given probability value when applied in the DistributionFunction(Int32).
Remarks
The Inverse Cumulative Distribution Function (ICDF) specifies, for a given probability, the value which the random variable will be at, or below, with that probability.
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InnerLogProbabilityMassFunction(Int32)

Gets the log-probability mass function (pmf) for this distribution evaluated at point x.
Declaration
protected virtual double InnerLogProbabilityMassFunction(int k)
Parameters
Type Name Description
System.Int32 k A single point in the distribution range.
Returns
Type Description
System.Double The logarithm of the probability of x occurring in the current distribution.
Remarks
The Probability Mass Function (PMF) describes the probability that a given value k will occur.
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InnerProbabilityMassFunction(Int32)

Gets the probability mass function (pmf) for this distribution evaluated at point x.
Declaration
protected abstract double InnerProbabilityMassFunction(int k)
Parameters
Type Name Description
System.Int32 k A single point in the distribution range.
Returns
Type Description
System.Double The probability of k occurring in the current distribution.
Remarks
The Probability Mass Function (PMF) describes the probability that a given value x will occur.
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InverseDistributionFunction(Double)

Gets the inverse of the cumulative distribution function (icdf) for this distribution evaluated at probability p. This function is also known as the Quantile function.
Declaration
public int InverseDistributionFunction(double p)
Parameters
Type Name Description
System.Double p A probability value between 0 and 1.
Returns
Type Description
System.Int32 A sample which could original the given probability value when applied in the DistributionFunction(Int32).
Remarks
The Inverse Cumulative Distribution Function (ICDF) specifies, for a given probability, the value which the random variable will be at, or below, with that probability.
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LogCumulativeHazardFunction(Int32)

Gets the log-cumulative hazard function for this distribution evaluated at point x.
Declaration
public virtual double LogCumulativeHazardFunction(int x)
Parameters
Type Name Description
System.Int32 x A single point in the distribution range.
Returns
Type Description
System.Double The logarithm of the cumulative hazard function H(x) evaluated at x in the current distribution.
Remarks

A probability distribution identifies either the probability of each value of an unidentified random variable (when the variable is discrete), or the probability of the value falling within a particular interval (when the variable is continuous).

The probability distribution describes the range of possible values that a random variable can attain and the probability that the value of the random variable is within any (measurable) subset of that range.

The function describing the probability that a given discrete value will occur is called the probability function (or probability mass function, abbreviated PMF), and the function describing the cumulative probability that a given value or any value smaller than it will occur is called the distribution function (or cumulative distribution function, abbreviated CDF).

References:

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LogProbabilityMassFunction(Int32)

Gets the log-probability mass function (pmf) for this distribution evaluated at point x.
Declaration
public double LogProbabilityMassFunction(int k)
Parameters
Type Name Description
System.Int32 k A single point in the distribution range.
Returns
Type Description
System.Double The logarithm of the probability of x occurring in the current distribution.
Remarks
The Probability Mass Function (PMF) describes the probability that a given value k will occur.
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ProbabilityFunction(Double)

Abstract class for univariate discrete probability distributions.
Declaration
public double ProbabilityFunction(double x)
Parameters
Type Name Description
System.Double x
Returns
Type Description
System.Double
Remarks

A probability distribution identifies either the probability of each value of an unidentified random variable (when the variable is discrete), or the probability of the value falling within a particular interval (when the variable is continuous).

The probability distribution describes the range of possible values that a random variable can attain and the probability that the value of the random variable is within any (measurable) subset of that range.

The function describing the probability that a given discrete value will occur is called the probability function (or probability mass function, abbreviated PMF), and the function describing the cumulative probability that a given value or any value smaller than it will occur is called the distribution function (or cumulative distribution function, abbreviated CDF).

References:

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ProbabilityFunction(Double[])

Abstract class for univariate discrete probability distributions.
Declaration
public double ProbabilityFunction(double[] x)
Parameters
Type Name Description
System.Double[] x
Returns
Type Description
System.Double
Remarks

A probability distribution identifies either the probability of each value of an unidentified random variable (when the variable is discrete), or the probability of the value falling within a particular interval (when the variable is continuous).

The probability distribution describes the range of possible values that a random variable can attain and the probability that the value of the random variable is within any (measurable) subset of that range.

The function describing the probability that a given discrete value will occur is called the probability function (or probability mass function, abbreviated PMF), and the function describing the cumulative probability that a given value or any value smaller than it will occur is called the distribution function (or cumulative distribution function, abbreviated CDF).

References:

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ProbabilityFunction(Int32)

Abstract class for univariate discrete probability distributions.
Declaration
public double ProbabilityFunction(int x)
Parameters
Type Name Description
System.Int32 x
Returns
Type Description
System.Double
Remarks

A probability distribution identifies either the probability of each value of an unidentified random variable (when the variable is discrete), or the probability of the value falling within a particular interval (when the variable is continuous).

The probability distribution describes the range of possible values that a random variable can attain and the probability that the value of the random variable is within any (measurable) subset of that range.

The function describing the probability that a given discrete value will occur is called the probability function (or probability mass function, abbreviated PMF), and the function describing the cumulative probability that a given value or any value smaller than it will occur is called the distribution function (or cumulative distribution function, abbreviated CDF).

References:

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ProbabilityMassFunction(Int32)

Gets the probability mass function (pmf) for this distribution evaluated at point x.
Declaration
public double ProbabilityMassFunction(int k)
Parameters
Type Name Description
System.Int32 k A single point in the distribution range.
Returns
Type Description
System.Double The probability of k occurring in the current distribution.
Remarks
The Probability Mass Function (PMF) describes the probability that a given value x will occur.
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QuantileDensityFunction(Double)

Gets the first derivative of the inverse distribution function (icdf) for this distribution evaluated at probability p.
Declaration
public virtual double QuantileDensityFunction(double p)
Parameters
Type Name Description
System.Double p A probability value between 0 and 1.
Returns
Type Description
System.Double
Remarks

A probability distribution identifies either the probability of each value of an unidentified random variable (when the variable is discrete), or the probability of the value falling within a particular interval (when the variable is continuous).

The probability distribution describes the range of possible values that a random variable can attain and the probability that the value of the random variable is within any (measurable) subset of that range.

The function describing the probability that a given discrete value will occur is called the probability function (or probability mass function, abbreviated PMF), and the function describing the cumulative probability that a given value or any value smaller than it will occur is called the distribution function (or cumulative distribution function, abbreviated CDF).

References:

Explicit Interface Implementations

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IRandomNumberGenerator<Double>.Generate()

Abstract class for univariate discrete probability distributions.
Declaration
double IRandomNumberGenerator<double>.Generate()
Returns
Type Description
System.Double
Remarks

A probability distribution identifies either the probability of each value of an unidentified random variable (when the variable is discrete), or the probability of the value falling within a particular interval (when the variable is continuous).

The probability distribution describes the range of possible values that a random variable can attain and the probability that the value of the random variable is within any (measurable) subset of that range.

The function describing the probability that a given discrete value will occur is called the probability function (or probability mass function, abbreviated PMF), and the function describing the cumulative probability that a given value or any value smaller than it will occur is called the distribution function (or cumulative distribution function, abbreviated CDF).

References:

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IRandomNumberGenerator<Double>.Generate(Int32)

Abstract class for univariate discrete probability distributions.
Declaration
double[] IRandomNumberGenerator<double>.Generate(int samples)
Parameters
Type Name Description
System.Int32 samples
Returns
Type Description
System.Double[]
Remarks

A probability distribution identifies either the probability of each value of an unidentified random variable (when the variable is discrete), or the probability of the value falling within a particular interval (when the variable is continuous).

The probability distribution describes the range of possible values that a random variable can attain and the probability that the value of the random variable is within any (measurable) subset of that range.

The function describing the probability that a given discrete value will occur is called the probability function (or probability mass function, abbreviated PMF), and the function describing the cumulative probability that a given value or any value smaller than it will occur is called the distribution function (or cumulative distribution function, abbreviated CDF).

References:

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ISampleableDistribution<Double>.Generate(FastRandom)

Abstract class for univariate discrete probability distributions.
Declaration
double ISampleableDistribution<double>.Generate(FastRandom source)
Parameters
Type Name Description
Mars.Common.Core.Random.FastRandom source
Returns
Type Description
System.Double
Remarks

A probability distribution identifies either the probability of each value of an unidentified random variable (when the variable is discrete), or the probability of the value falling within a particular interval (when the variable is continuous).

The probability distribution describes the range of possible values that a random variable can attain and the probability that the value of the random variable is within any (measurable) subset of that range.

The function describing the probability that a given discrete value will occur is called the probability function (or probability mass function, abbreviated PMF), and the function describing the cumulative probability that a given value or any value smaller than it will occur is called the distribution function (or cumulative distribution function, abbreviated CDF).

References:

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ISampleableDistribution<Double>.Generate(Double, FastRandom)

Abstract class for univariate discrete probability distributions.
Declaration
double ISampleableDistribution<double>.Generate(double result, FastRandom source)
Parameters
Type Name Description
System.Double result
Mars.Common.Core.Random.FastRandom source
Returns
Type Description
System.Double
Remarks

A probability distribution identifies either the probability of each value of an unidentified random variable (when the variable is discrete), or the probability of the value falling within a particular interval (when the variable is continuous).

The probability distribution describes the range of possible values that a random variable can attain and the probability that the value of the random variable is within any (measurable) subset of that range.

The function describing the probability that a given discrete value will occur is called the probability function (or probability mass function, abbreviated PMF), and the function describing the cumulative probability that a given value or any value smaller than it will occur is called the distribution function (or cumulative distribution function, abbreviated CDF).

References:

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ISampleableDistribution<Double>.Generate(Double)

Abstract class for univariate discrete probability distributions.
Declaration
double ISampleableDistribution<double>.Generate(double result)
Parameters
Type Name Description
System.Double result
Returns
Type Description
System.Double
Remarks

A probability distribution identifies either the probability of each value of an unidentified random variable (when the variable is discrete), or the probability of the value falling within a particular interval (when the variable is continuous).

The probability distribution describes the range of possible values that a random variable can attain and the probability that the value of the random variable is within any (measurable) subset of that range.

The function describing the probability that a given discrete value will occur is called the probability function (or probability mass function, abbreviated PMF), and the function describing the cumulative probability that a given value or any value smaller than it will occur is called the distribution function (or cumulative distribution function, abbreviated CDF).

References:

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ISampleableDistribution<Double>.Generate(Int32, FastRandom)

Abstract class for univariate discrete probability distributions.
Declaration
double[] ISampleableDistribution<double>.Generate(int samples, FastRandom source)
Parameters
Type Name Description
System.Int32 samples
Mars.Common.Core.Random.FastRandom source
Returns
Type Description
System.Double[]
Remarks

A probability distribution identifies either the probability of each value of an unidentified random variable (when the variable is discrete), or the probability of the value falling within a particular interval (when the variable is continuous).

The probability distribution describes the range of possible values that a random variable can attain and the probability that the value of the random variable is within any (measurable) subset of that range.

The function describing the probability that a given discrete value will occur is called the probability function (or probability mass function, abbreviated PMF), and the function describing the cumulative probability that a given value or any value smaller than it will occur is called the distribution function (or cumulative distribution function, abbreviated CDF).

References:

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ISampleableDistribution<Int32>.Generate(Int32, FastRandom)

Abstract class for univariate discrete probability distributions.
Declaration
int ISampleableDistribution<int>.Generate(int result, FastRandom source)
Parameters
Type Name Description
System.Int32 result
Mars.Common.Core.Random.FastRandom source
Returns
Type Description
System.Int32
Remarks

A probability distribution identifies either the probability of each value of an unidentified random variable (when the variable is discrete), or the probability of the value falling within a particular interval (when the variable is continuous).

The probability distribution describes the range of possible values that a random variable can attain and the probability that the value of the random variable is within any (measurable) subset of that range.

The function describing the probability that a given discrete value will occur is called the probability function (or probability mass function, abbreviated PMF), and the function describing the cumulative probability that a given value or any value smaller than it will occur is called the distribution function (or cumulative distribution function, abbreviated CDF).

References:

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ISampleableDistribution<Int32>.Generate(Int32)

Abstract class for univariate discrete probability distributions.
Declaration
int ISampleableDistribution<int>.Generate(int result)
Parameters
Type Name Description
System.Int32 result
Returns
Type Description
System.Int32
Remarks

A probability distribution identifies either the probability of each value of an unidentified random variable (when the variable is discrete), or the probability of the value falling within a particular interval (when the variable is continuous).

The probability distribution describes the range of possible values that a random variable can attain and the probability that the value of the random variable is within any (measurable) subset of that range.

The function describing the probability that a given discrete value will occur is called the probability function (or probability mass function, abbreviated PMF), and the function describing the cumulative probability that a given value or any value smaller than it will occur is called the distribution function (or cumulative distribution function, abbreviated CDF).

References:

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IUnivariateDistribution<Double>.CumulativeHazardFunction(Double)

Abstract class for univariate discrete probability distributions.
Declaration
double IUnivariateDistribution<double>.CumulativeHazardFunction(double x)
Parameters
Type Name Description
System.Double x
Returns
Type Description
System.Double
Remarks

A probability distribution identifies either the probability of each value of an unidentified random variable (when the variable is discrete), or the probability of the value falling within a particular interval (when the variable is continuous).

The probability distribution describes the range of possible values that a random variable can attain and the probability that the value of the random variable is within any (measurable) subset of that range.

The function describing the probability that a given discrete value will occur is called the probability function (or probability mass function, abbreviated PMF), and the function describing the cumulative probability that a given value or any value smaller than it will occur is called the distribution function (or cumulative distribution function, abbreviated CDF).

References:

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IUnivariateDistribution<Double>.HazardFunction(Double)

Abstract class for univariate discrete probability distributions.
Declaration
double IUnivariateDistribution<double>.HazardFunction(double x)
Parameters
Type Name Description
System.Double x
Returns
Type Description
System.Double
Remarks

A probability distribution identifies either the probability of each value of an unidentified random variable (when the variable is discrete), or the probability of the value falling within a particular interval (when the variable is continuous).

The probability distribution describes the range of possible values that a random variable can attain and the probability that the value of the random variable is within any (measurable) subset of that range.

The function describing the probability that a given discrete value will occur is called the probability function (or probability mass function, abbreviated PMF), and the function describing the cumulative probability that a given value or any value smaller than it will occur is called the distribution function (or cumulative distribution function, abbreviated CDF).

References:

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IUnivariateDistribution<Double>.InverseDistributionFunction(Double)

Abstract class for univariate discrete probability distributions.
Declaration
double IUnivariateDistribution<double>.InverseDistributionFunction(double p)
Parameters
Type Name Description
System.Double p
Returns
Type Description
System.Double
Remarks

A probability distribution identifies either the probability of each value of an unidentified random variable (when the variable is discrete), or the probability of the value falling within a particular interval (when the variable is continuous).

The probability distribution describes the range of possible values that a random variable can attain and the probability that the value of the random variable is within any (measurable) subset of that range.

The function describing the probability that a given discrete value will occur is called the probability function (or probability mass function, abbreviated PMF), and the function describing the cumulative probability that a given value or any value smaller than it will occur is called the distribution function (or cumulative distribution function, abbreviated CDF).

References:

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IUnivariateDistribution<Double>.Support

Gets the support interval for this distribution.
Declaration
DoubleRange IUnivariateDistribution<double>.Support { get; }
Returns
Type Description
DoubleRange A DoubleRange containing the support interval for this distribution.
Remarks

A probability distribution identifies either the probability of each value of an unidentified random variable (when the variable is discrete), or the probability of the value falling within a particular interval (when the variable is continuous).

The probability distribution describes the range of possible values that a random variable can attain and the probability that the value of the random variable is within any (measurable) subset of that range.

The function describing the probability that a given discrete value will occur is called the probability function (or probability mass function, abbreviated PMF), and the function describing the cumulative probability that a given value or any value smaller than it will occur is called the distribution function (or cumulative distribution function, abbreviated CDF).

References:

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IUnivariateDistribution<Int32>.Support

Gets the support interval for this distribution.
Declaration
DoubleRange IUnivariateDistribution<int>.Support { get; }
Returns
Type Description
DoubleRange A DoubleRange containing the support interval for this distribution.
Remarks

A probability distribution identifies either the probability of each value of an unidentified random variable (when the variable is discrete), or the probability of the value falling within a particular interval (when the variable is continuous).

The probability distribution describes the range of possible values that a random variable can attain and the probability that the value of the random variable is within any (measurable) subset of that range.

The function describing the probability that a given discrete value will occur is called the probability function (or probability mass function, abbreviated PMF), and the function describing the cumulative probability that a given value or any value smaller than it will occur is called the distribution function (or cumulative distribution function, abbreviated CDF).

References:

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IUnivariateDistribution.GetRange(Double)

Gets the distribution range within a given percentile.
Declaration
DoubleRange IUnivariateDistribution.GetRange(double percentile)
Parameters
Type Name Description
System.Double percentile The percentile at which the distribution ranges will be returned.
Returns
Type Description
DoubleRange A DoubleRange object containing the minimum value for the distribution value, and the third quartile (Q2) as the maximum.
Remarks
If 0.25 is passed as the percentile argument, this function returns the same as the Quartiles function.
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IUnivariateDistribution.Support

Gets the support interval for this distribution.
Declaration
DoubleRange IUnivariateDistribution.Support { get; }
Returns
Type Description
DoubleRange A DoubleRange containing the support interval for this distribution.
Remarks

A probability distribution identifies either the probability of each value of an unidentified random variable (when the variable is discrete), or the probability of the value falling within a particular interval (when the variable is continuous).

The probability distribution describes the range of possible values that a random variable can attain and the probability that the value of the random variable is within any (measurable) subset of that range.

The function describing the probability that a given discrete value will occur is called the probability function (or probability mass function, abbreviated PMF), and the function describing the cumulative probability that a given value or any value smaller than it will occur is called the distribution function (or cumulative distribution function, abbreviated CDF).

References:

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IDistribution.DistributionFunction(Double[])

Gets the probability density function (pdf) for this distribution evaluated at point x.
Declaration
double IDistribution.DistributionFunction(double[] x)
Parameters
Type Name Description
System.Double[] x A single point in the distribution range. For a univariate distribution, this should be a single double value. For a multivariate distribution, this should be a double array.
Returns
Type Description
System.Double The probability of x occurring in the current distribution.
Remarks
The Probability Density Function (PDF) describes the probability that a given value x will occur.
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IDistribution.ProbabilityFunction(Double[])

Abstract class for univariate discrete probability distributions.
Declaration
double IDistribution.ProbabilityFunction(double[] x)
Parameters
Type Name Description
System.Double[] x
Returns
Type Description
System.Double
Remarks

A probability distribution identifies either the probability of each value of an unidentified random variable (when the variable is discrete), or the probability of the value falling within a particular interval (when the variable is continuous).

The probability distribution describes the range of possible values that a random variable can attain and the probability that the value of the random variable is within any (measurable) subset of that range.

The function describing the probability that a given discrete value will occur is called the probability function (or probability mass function, abbreviated PMF), and the function describing the cumulative probability that a given value or any value smaller than it will occur is called the distribution function (or cumulative distribution function, abbreviated CDF).

References:

Implements

System.IFormattable
System.ICloneable
Mars.Common.Core.Random.IRandomNumberGenerator<T>
Mars.Common.Core.Random.IRandomNumberGenerator<T>

Extension Methods