Class UniformDiscreteDistribution

Discrete uniform distribution.
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
Assembly: Mars.Numerics.dll
Syntax
[Serializable]
public class UniformDiscreteDistribution : UnivariateDiscreteDistribution, IFormattable, IUnivariateDistribution<int>, IUnivariateDistribution, IDistribution, ICloneable, IUnivariateDistribution<double>, ISampleableDistribution<double>, IRandomNumberGenerator<double>, ISampleableDistribution<int>, IRandomNumberGenerator<int>
Remarks

In probability theory and statistics, the discrete uniform distribution is a symmetric probability distribution whereby a finite number of values are equally likely to be observed; every one of n values has equal probability 1/n. Another way of saying "discrete uniform distribution" would be "a known, finite number of outcomes equally likely to happen".

A simple example of the discrete uniform distribution is throwing a fair die. The possible values are 1, 2, 3, 4, 5, 6, and each time the die is thrown the probability of a given score is 1/6. If two dice are thrown and their values added, the resulting distribution is no longer uniform since not all sums have equal probability.

The discrete uniform distribution itself is inherently non-parametric. It is convenient, however, to represent its values generally by an integer interval [a,b], so that a,b become the main parameters of the distribution (often one simply considers the interval [1,n] with the single parameter n).

References:

Examples
// Create an uniform (discrete) distribution in [2, 6] 
var dist = new UniformDiscreteDistribution(a: 2, b: 6);

// Common measures
double mean = dist.Mean;     // 4.0
double median = dist.Median; // 4.0
double var = dist.Variance;  // 1.3333333333333333

// Cumulative distribution functions
double cdf = dist.DistributionFunction(k: 2);               // 0.2
double ccdf = dist.ComplementaryDistributionFunction(k: 2); // 0.8

// Probability mass functions
double pmf1 = dist.ProbabilityMassFunction(k: 4); // 0.2
double pmf2 = dist.ProbabilityMassFunction(k: 5); // 0.2
double pmf3 = dist.ProbabilityMassFunction(k: 6); // 0.2
double lpmf = dist.LogProbabilityMassFunction(k: 2); // -1.6094379124341003

// Quantile function
int icdf1 = dist.InverseDistributionFunction(p: 0.17); // 2
int icdf2 = dist.InverseDistributionFunction(p: 0.46); // 4
int icdf3 = dist.InverseDistributionFunction(p: 0.87); // 6

// Hazard (failure rate) functions
double hf = dist.HazardFunction(x: 4); // 0.5
double chf = dist.CumulativeHazardFunction(x: 4); // 0.916290731874155

// String representation
string str = dist.ToString(CultureInfo.InvariantCulture); // "U(x; a = 2, b = 6)"

Constructors

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UniformDiscreteDistribution(Int32, Int32)

Creates a discrete uniform distribution defined in the interval [a;b].
Declaration
public UniformDiscreteDistribution(int a = 0, int b = 1)
Parameters
Type Name Description
System.Int32 a The starting (minimum) value a.
System.Int32 b The ending (maximum) value b.
Remarks

In probability theory and statistics, the discrete uniform distribution is a symmetric probability distribution whereby a finite number of values are equally likely to be observed; every one of n values has equal probability 1/n. Another way of saying "discrete uniform distribution" would be "a known, finite number of outcomes equally likely to happen".

A simple example of the discrete uniform distribution is throwing a fair die. The possible values are 1, 2, 3, 4, 5, 6, and each time the die is thrown the probability of a given score is 1/6. If two dice are thrown and their values added, the resulting distribution is no longer uniform since not all sums have equal probability.

The discrete uniform distribution itself is inherently non-parametric. It is convenient, however, to represent its values generally by an integer interval [a,b], so that a,b become the main parameters of the distribution (often one simply considers the interval [1,n] with the single parameter n).

References:

Properties

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Entropy

Gets the entropy for this distribution.
Declaration
public override double Entropy { get; }
Property Value
Type Description
System.Double
Overrides
Remarks

In probability theory and statistics, the discrete uniform distribution is a symmetric probability distribution whereby a finite number of values are equally likely to be observed; every one of n values has equal probability 1/n. Another way of saying "discrete uniform distribution" would be "a known, finite number of outcomes equally likely to happen".

A simple example of the discrete uniform distribution is throwing a fair die. The possible values are 1, 2, 3, 4, 5, 6, and each time the die is thrown the probability of a given score is 1/6. If two dice are thrown and their values added, the resulting distribution is no longer uniform since not all sums have equal probability.

The discrete uniform distribution itself is inherently non-parametric. It is convenient, however, to represent its values generally by an integer interval [a,b], so that a,b become the main parameters of the distribution (often one simply considers the interval [1,n] with the single parameter n).

References:

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Length

Gets the length of the distribution (b - a + 1).
Declaration
public double Length { get; }
Property Value
Type Description
System.Double
Remarks

In probability theory and statistics, the discrete uniform distribution is a symmetric probability distribution whereby a finite number of values are equally likely to be observed; every one of n values has equal probability 1/n. Another way of saying "discrete uniform distribution" would be "a known, finite number of outcomes equally likely to happen".

A simple example of the discrete uniform distribution is throwing a fair die. The possible values are 1, 2, 3, 4, 5, 6, and each time the die is thrown the probability of a given score is 1/6. If two dice are thrown and their values added, the resulting distribution is no longer uniform since not all sums have equal probability.

The discrete uniform distribution itself is inherently non-parametric. It is convenient, however, to represent its values generally by an integer interval [a,b], so that a,b become the main parameters of the distribution (often one simply considers the interval [1,n] with the single parameter n).

References:

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Maximum

Gets the maximum value of the distribution (b).
Declaration
public double Maximum { get; }
Property Value
Type Description
System.Double
Remarks

In probability theory and statistics, the discrete uniform distribution is a symmetric probability distribution whereby a finite number of values are equally likely to be observed; every one of n values has equal probability 1/n. Another way of saying "discrete uniform distribution" would be "a known, finite number of outcomes equally likely to happen".

A simple example of the discrete uniform distribution is throwing a fair die. The possible values are 1, 2, 3, 4, 5, 6, and each time the die is thrown the probability of a given score is 1/6. If two dice are thrown and their values added, the resulting distribution is no longer uniform since not all sums have equal probability.

The discrete uniform distribution itself is inherently non-parametric. It is convenient, however, to represent its values generally by an integer interval [a,b], so that a,b become the main parameters of the distribution (often one simply considers the interval [1,n] with the single parameter n).

References:

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Mean

Gets the mean for this distribution.
Declaration
public override double Mean { get; }
Property Value
Type Description
System.Double
Overrides
Remarks

In probability theory and statistics, the discrete uniform distribution is a symmetric probability distribution whereby a finite number of values are equally likely to be observed; every one of n values has equal probability 1/n. Another way of saying "discrete uniform distribution" would be "a known, finite number of outcomes equally likely to happen".

A simple example of the discrete uniform distribution is throwing a fair die. The possible values are 1, 2, 3, 4, 5, 6, and each time the die is thrown the probability of a given score is 1/6. If two dice are thrown and their values added, the resulting distribution is no longer uniform since not all sums have equal probability.

The discrete uniform distribution itself is inherently non-parametric. It is convenient, however, to represent its values generally by an integer interval [a,b], so that a,b become the main parameters of the distribution (often one simply considers the interval [1,n] with the single parameter n).

References:

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Minimum

Gets the minimum value of the distribution (a).
Declaration
public double Minimum { get; }
Property Value
Type Description
System.Double
Remarks

In probability theory and statistics, the discrete uniform distribution is a symmetric probability distribution whereby a finite number of values are equally likely to be observed; every one of n values has equal probability 1/n. Another way of saying "discrete uniform distribution" would be "a known, finite number of outcomes equally likely to happen".

A simple example of the discrete uniform distribution is throwing a fair die. The possible values are 1, 2, 3, 4, 5, 6, and each time the die is thrown the probability of a given score is 1/6. If two dice are thrown and their values added, the resulting distribution is no longer uniform since not all sums have equal probability.

The discrete uniform distribution itself is inherently non-parametric. It is convenient, however, to represent its values generally by an integer interval [a,b], so that a,b become the main parameters of the distribution (often one simply considers the interval [1,n] with the single parameter n).

References:

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Support

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

In probability theory and statistics, the discrete uniform distribution is a symmetric probability distribution whereby a finite number of values are equally likely to be observed; every one of n values has equal probability 1/n. Another way of saying "discrete uniform distribution" would be "a known, finite number of outcomes equally likely to happen".

A simple example of the discrete uniform distribution is throwing a fair die. The possible values are 1, 2, 3, 4, 5, 6, and each time the die is thrown the probability of a given score is 1/6. If two dice are thrown and their values added, the resulting distribution is no longer uniform since not all sums have equal probability.

The discrete uniform distribution itself is inherently non-parametric. It is convenient, however, to represent its values generally by an integer interval [a,b], so that a,b become the main parameters of the distribution (often one simply considers the interval [1,n] with the single parameter n).

References:

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Variance

Gets the variance for this distribution.
Declaration
public override double Variance { get; }
Property Value
Type Description
System.Double
Overrides
Remarks

In probability theory and statistics, the discrete uniform distribution is a symmetric probability distribution whereby a finite number of values are equally likely to be observed; every one of n values has equal probability 1/n. Another way of saying "discrete uniform distribution" would be "a known, finite number of outcomes equally likely to happen".

A simple example of the discrete uniform distribution is throwing a fair die. The possible values are 1, 2, 3, 4, 5, 6, and each time the die is thrown the probability of a given score is 1/6. If two dice are thrown and their values added, the resulting distribution is no longer uniform since not all sums have equal probability.

The discrete uniform distribution itself is inherently non-parametric. It is convenient, however, to represent its values generally by an integer interval [a,b], so that a,b become the main parameters of the distribution (often one simply considers the interval [1,n] with the single parameter n).

References:

Methods

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Clone()

Creates a new object that is a copy of the current instance.
Declaration
public override object Clone()
Returns
Type Description
System.Object A new object that is a copy of this instance.
Overrides
Remarks

In probability theory and statistics, the discrete uniform distribution is a symmetric probability distribution whereby a finite number of values are equally likely to be observed; every one of n values has equal probability 1/n. Another way of saying "discrete uniform distribution" would be "a known, finite number of outcomes equally likely to happen".

A simple example of the discrete uniform distribution is throwing a fair die. The possible values are 1, 2, 3, 4, 5, 6, and each time the die is thrown the probability of a given score is 1/6. If two dice are thrown and their values added, the resulting distribution is no longer uniform since not all sums have equal probability.

The discrete uniform distribution itself is inherently non-parametric. It is convenient, however, to represent its values generally by an integer interval [a,b], so that a,b become the main parameters of the distribution (often one simply considers the interval [1,n] with the single parameter n).

References:

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Generate(FastRandom)

Generates a random observation from the current distribution.
Declaration
public override 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.
Overrides
Remarks

In probability theory and statistics, the discrete uniform distribution is a symmetric probability distribution whereby a finite number of values are equally likely to be observed; every one of n values has equal probability 1/n. Another way of saying "discrete uniform distribution" would be "a known, finite number of outcomes equally likely to happen".

A simple example of the discrete uniform distribution is throwing a fair die. The possible values are 1, 2, 3, 4, 5, 6, and each time the die is thrown the probability of a given score is 1/6. If two dice are thrown and their values added, the resulting distribution is no longer uniform since not all sums have equal probability.

The discrete uniform distribution itself is inherently non-parametric. It is convenient, however, to represent its values generally by an integer interval [a,b], so that a,b become the main parameters of the distribution (often one simply considers the interval [1,n] with the single parameter n).

References:

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Generate(Int32, Int32[], FastRandom)

Generates a random vector of observations from the current distribution.
Declaration
public override 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 Mars.Common.Core.Random.Generator.Random.
Returns
Type Description
System.Int32[] A random vector of observations drawn from this distribution.
Overrides
Remarks

In probability theory and statistics, the discrete uniform distribution is a symmetric probability distribution whereby a finite number of values are equally likely to be observed; every one of n values has equal probability 1/n. Another way of saying "discrete uniform distribution" would be "a known, finite number of outcomes equally likely to happen".

A simple example of the discrete uniform distribution is throwing a fair die. The possible values are 1, 2, 3, 4, 5, 6, and each time the die is thrown the probability of a given score is 1/6. If two dice are thrown and their values added, the resulting distribution is no longer uniform since not all sums have equal probability.

The discrete uniform distribution itself is inherently non-parametric. It is convenient, however, to represent its values generally by an integer interval [a,b], so that a,b become the main parameters of the distribution (often one simply considers the interval [1,n] with the single parameter n).

References:

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InnerDistributionFunction(Int32)

Gets the cumulative distribution function (cdf) for this distribution evaluated at point k.
Declaration
protected override double InnerDistributionFunction(int k)
Parameters
Type Name Description
System.Int32 k A single point in the distribution range.
Returns
Type Description
System.Double
Overrides
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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InnerLogProbabilityMassFunction(Int32)

Gets the log-probability mass function (pmf) for this distribution evaluated at point x.
Declaration
protected override 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 k occurring in the current distribution.
Overrides
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 override 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.
Overrides
Remarks
The Probability Mass Function (PMF) describes the probability that a given value k will occur.
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Random()

Generates a random observation from the Uniform distribution defined in the interval 0 and MAXVALUE.
Declaration
public static int Random()
Returns
Type Description
System.Int32 A random double value sampled from the specified Uniform distribution.
Remarks

In probability theory and statistics, the discrete uniform distribution is a symmetric probability distribution whereby a finite number of values are equally likely to be observed; every one of n values has equal probability 1/n. Another way of saying "discrete uniform distribution" would be "a known, finite number of outcomes equally likely to happen".

A simple example of the discrete uniform distribution is throwing a fair die. The possible values are 1, 2, 3, 4, 5, 6, and each time the die is thrown the probability of a given score is 1/6. If two dice are thrown and their values added, the resulting distribution is no longer uniform since not all sums have equal probability.

The discrete uniform distribution itself is inherently non-parametric. It is convenient, however, to represent its values generally by an integer interval [a,b], so that a,b become the main parameters of the distribution (often one simply considers the interval [1,n] with the single parameter n).

References:

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Random(FastRandom)

Generates a random observation from the Uniform distribution defined in the interval 0 and MAXVALUE.
Declaration
public static int Random(FastRandom source)
Parameters
Type Name Description
Mars.Common.Core.Random.FastRandom source
Returns
Type Description
System.Int32 A random double value sampled from the specified Uniform distribution.
Remarks

In probability theory and statistics, the discrete uniform distribution is a symmetric probability distribution whereby a finite number of values are equally likely to be observed; every one of n values has equal probability 1/n. Another way of saying "discrete uniform distribution" would be "a known, finite number of outcomes equally likely to happen".

A simple example of the discrete uniform distribution is throwing a fair die. The possible values are 1, 2, 3, 4, 5, 6, and each time the die is thrown the probability of a given score is 1/6. If two dice are thrown and their values added, the resulting distribution is no longer uniform since not all sums have equal probability.

The discrete uniform distribution itself is inherently non-parametric. It is convenient, however, to represent its values generally by an integer interval [a,b], so that a,b become the main parameters of the distribution (often one simply considers the interval [1,n] with the single parameter n).

References:

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Random(Int32, FastRandom)

Generates a random observation from the Uniform distribution defined in the interval 0 and MAXVALUE.
Declaration
public static int[] Random(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[] An array of double values sampled from the specified Uniform distribution.
Remarks

In probability theory and statistics, the discrete uniform distribution is a symmetric probability distribution whereby a finite number of values are equally likely to be observed; every one of n values has equal probability 1/n. Another way of saying "discrete uniform distribution" would be "a known, finite number of outcomes equally likely to happen".

A simple example of the discrete uniform distribution is throwing a fair die. The possible values are 1, 2, 3, 4, 5, 6, and each time the die is thrown the probability of a given score is 1/6. If two dice are thrown and their values added, the resulting distribution is no longer uniform since not all sums have equal probability.

The discrete uniform distribution itself is inherently non-parametric. It is convenient, however, to represent its values generally by an integer interval [a,b], so that a,b become the main parameters of the distribution (often one simply considers the interval [1,n] with the single parameter n).

References:

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Random(Int32, Int32, FastRandom)

Generates a random observation from the Uniform distribution with the given parameters.
Declaration
public static int Random(int a, int b, FastRandom source)
Parameters
Type Name Description
System.Int32 a The starting number a.
System.Int32 b The ending number b.
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 double value sampled from the specified Uniform distribution.
Remarks

In probability theory and statistics, the discrete uniform distribution is a symmetric probability distribution whereby a finite number of values are equally likely to be observed; every one of n values has equal probability 1/n. Another way of saying "discrete uniform distribution" would be "a known, finite number of outcomes equally likely to happen".

A simple example of the discrete uniform distribution is throwing a fair die. The possible values are 1, 2, 3, 4, 5, 6, and each time the die is thrown the probability of a given score is 1/6. If two dice are thrown and their values added, the resulting distribution is no longer uniform since not all sums have equal probability.

The discrete uniform distribution itself is inherently non-parametric. It is convenient, however, to represent its values generally by an integer interval [a,b], so that a,b become the main parameters of the distribution (often one simply considers the interval [1,n] with the single parameter n).

References:

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Random(Int32, Int32, Int32, FastRandom)

Generates a random vector of observations from the Uniform distribution with the given parameters.
Declaration
public static int[] Random(int a, int b, int samples, FastRandom source)
Parameters
Type Name Description
System.Int32 a The starting number a.
System.Int32 b The ending number b.
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[] An array of double values sampled from the specified Uniform distribution.
Remarks

In probability theory and statistics, the discrete uniform distribution is a symmetric probability distribution whereby a finite number of values are equally likely to be observed; every one of n values has equal probability 1/n. Another way of saying "discrete uniform distribution" would be "a known, finite number of outcomes equally likely to happen".

A simple example of the discrete uniform distribution is throwing a fair die. The possible values are 1, 2, 3, 4, 5, 6, and each time the die is thrown the probability of a given score is 1/6. If two dice are thrown and their values added, the resulting distribution is no longer uniform since not all sums have equal probability.

The discrete uniform distribution itself is inherently non-parametric. It is convenient, however, to represent its values generally by an integer interval [a,b], so that a,b become the main parameters of the distribution (often one simply considers the interval [1,n] with the single parameter n).

References:

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Random(Int32, Int32, Int32, Int32[], FastRandom)

Generates a random vector of observations from the Uniform distribution with the given parameters.
Declaration
public static int[] Random(int a, int b, int samples, int[] result, FastRandom source)
Parameters
Type Name Description
System.Int32 a The starting number a.
System.Int32 b The ending number b.
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[] An array of double values sampled from the specified Uniform distribution.
Remarks

In probability theory and statistics, the discrete uniform distribution is a symmetric probability distribution whereby a finite number of values are equally likely to be observed; every one of n values has equal probability 1/n. Another way of saying "discrete uniform distribution" would be "a known, finite number of outcomes equally likely to happen".

A simple example of the discrete uniform distribution is throwing a fair die. The possible values are 1, 2, 3, 4, 5, 6, and each time the die is thrown the probability of a given score is 1/6. If two dice are thrown and their values added, the resulting distribution is no longer uniform since not all sums have equal probability.

The discrete uniform distribution itself is inherently non-parametric. It is convenient, however, to represent its values generally by an integer interval [a,b], so that a,b become the main parameters of the distribution (often one simply considers the interval [1,n] with the single parameter n).

References:

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Random(Int32, Int32, Int32, Int32[])

Generates a random vector of observations from the Uniform distribution with the given parameters.
Declaration
public static int[] Random(int a, int b, int samples, int[] result)
Parameters
Type Name Description
System.Int32 a The starting number a.
System.Int32 b The ending number b.
System.Int32 samples The number of samples to generate.
System.Int32[] result The location where to store the samples.
Returns
Type Description
System.Int32[] An array of double values sampled from the specified Uniform distribution.
Remarks

In probability theory and statistics, the discrete uniform distribution is a symmetric probability distribution whereby a finite number of values are equally likely to be observed; every one of n values has equal probability 1/n. Another way of saying "discrete uniform distribution" would be "a known, finite number of outcomes equally likely to happen".

A simple example of the discrete uniform distribution is throwing a fair die. The possible values are 1, 2, 3, 4, 5, 6, and each time the die is thrown the probability of a given score is 1/6. If two dice are thrown and their values added, the resulting distribution is no longer uniform since not all sums have equal probability.

The discrete uniform distribution itself is inherently non-parametric. It is convenient, however, to represent its values generally by an integer interval [a,b], so that a,b become the main parameters of the distribution (often one simply considers the interval [1,n] with the single parameter n).

References:

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Random(Int32, Int32, Int32)

Generates a random vector of observations from the Uniform distribution with the given parameters.
Declaration
public static int[] Random(int a, int b, int samples)
Parameters
Type Name Description
System.Int32 a The starting number a.
System.Int32 b The ending number b.
System.Int32 samples The number of samples to generate.
Returns
Type Description
System.Int32[] An array of double values sampled from the specified Uniform distribution.
Remarks

In probability theory and statistics, the discrete uniform distribution is a symmetric probability distribution whereby a finite number of values are equally likely to be observed; every one of n values has equal probability 1/n. Another way of saying "discrete uniform distribution" would be "a known, finite number of outcomes equally likely to happen".

A simple example of the discrete uniform distribution is throwing a fair die. The possible values are 1, 2, 3, 4, 5, 6, and each time the die is thrown the probability of a given score is 1/6. If two dice are thrown and their values added, the resulting distribution is no longer uniform since not all sums have equal probability.

The discrete uniform distribution itself is inherently non-parametric. It is convenient, however, to represent its values generally by an integer interval [a,b], so that a,b become the main parameters of the distribution (often one simply considers the interval [1,n] with the single parameter n).

References:

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Random(Int32, Int32)

Generates a random observation from the Uniform distribution with the given parameters.
Declaration
public static int Random(int a, int b)
Parameters
Type Name Description
System.Int32 a The starting number a.
System.Int32 b The ending number b.
Returns
Type Description
System.Int32 A random double value sampled from the specified Uniform distribution.
Remarks

In probability theory and statistics, the discrete uniform distribution is a symmetric probability distribution whereby a finite number of values are equally likely to be observed; every one of n values has equal probability 1/n. Another way of saying "discrete uniform distribution" would be "a known, finite number of outcomes equally likely to happen".

A simple example of the discrete uniform distribution is throwing a fair die. The possible values are 1, 2, 3, 4, 5, 6, and each time the die is thrown the probability of a given score is 1/6. If two dice are thrown and their values added, the resulting distribution is no longer uniform since not all sums have equal probability.

The discrete uniform distribution itself is inherently non-parametric. It is convenient, however, to represent its values generally by an integer interval [a,b], so that a,b become the main parameters of the distribution (often one simply considers the interval [1,n] with the single parameter n).

References:

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Random(Int32, Int32[], FastRandom)

Generates a random observation from the Uniform distribution defined in the interval 0 and MAXVALUE.
Declaration
public static int[] Random(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[] An array of double values sampled from the specified Uniform distribution.
Remarks

In probability theory and statistics, the discrete uniform distribution is a symmetric probability distribution whereby a finite number of values are equally likely to be observed; every one of n values has equal probability 1/n. Another way of saying "discrete uniform distribution" would be "a known, finite number of outcomes equally likely to happen".

A simple example of the discrete uniform distribution is throwing a fair die. The possible values are 1, 2, 3, 4, 5, 6, and each time the die is thrown the probability of a given score is 1/6. If two dice are thrown and their values added, the resulting distribution is no longer uniform since not all sums have equal probability.

The discrete uniform distribution itself is inherently non-parametric. It is convenient, however, to represent its values generally by an integer interval [a,b], so that a,b become the main parameters of the distribution (often one simply considers the interval [1,n] with the single parameter n).

References:

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Random(Int32, Int32[])

Generates a random observation from the Uniform distribution defined in the interval 0 and MAXVALUE.
Declaration
public static int[] Random(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[] An array of double values sampled from the specified Uniform distribution.
Remarks

In probability theory and statistics, the discrete uniform distribution is a symmetric probability distribution whereby a finite number of values are equally likely to be observed; every one of n values has equal probability 1/n. Another way of saying "discrete uniform distribution" would be "a known, finite number of outcomes equally likely to happen".

A simple example of the discrete uniform distribution is throwing a fair die. The possible values are 1, 2, 3, 4, 5, 6, and each time the die is thrown the probability of a given score is 1/6. If two dice are thrown and their values added, the resulting distribution is no longer uniform since not all sums have equal probability.

The discrete uniform distribution itself is inherently non-parametric. It is convenient, however, to represent its values generally by an integer interval [a,b], so that a,b become the main parameters of the distribution (often one simply considers the interval [1,n] with the single parameter n).

References:

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Random(Int32)

Generates a random observation from the Uniform distribution defined in the interval 0 and MAXVALUE.
Declaration
public static int[] Random(int samples)
Parameters
Type Name Description
System.Int32 samples The number of samples to generate.
Returns
Type Description
System.Int32[] An array of double values sampled from the specified Uniform distribution.
Remarks

In probability theory and statistics, the discrete uniform distribution is a symmetric probability distribution whereby a finite number of values are equally likely to be observed; every one of n values has equal probability 1/n. Another way of saying "discrete uniform distribution" would be "a known, finite number of outcomes equally likely to happen".

A simple example of the discrete uniform distribution is throwing a fair die. The possible values are 1, 2, 3, 4, 5, 6, and each time the die is thrown the probability of a given score is 1/6. If two dice are thrown and their values added, the resulting distribution is no longer uniform since not all sums have equal probability.

The discrete uniform distribution itself is inherently non-parametric. It is convenient, however, to represent its values generally by an integer interval [a,b], so that a,b become the main parameters of the distribution (often one simply considers the interval [1,n] with the single parameter n).

References:

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ToString(String, IFormatProvider)

Returns a System.String that represents this instance.
Declaration
public override string ToString(string format, IFormatProvider formatProvider = null)
Parameters
Type Name Description
System.String format
System.IFormatProvider formatProvider
Returns
Type Description
System.String A System.String that represents this instance.
Overrides
Remarks

In probability theory and statistics, the discrete uniform distribution is a symmetric probability distribution whereby a finite number of values are equally likely to be observed; every one of n values has equal probability 1/n. Another way of saying "discrete uniform distribution" would be "a known, finite number of outcomes equally likely to happen".

A simple example of the discrete uniform distribution is throwing a fair die. The possible values are 1, 2, 3, 4, 5, 6, and each time the die is thrown the probability of a given score is 1/6. If two dice are thrown and their values added, the resulting distribution is no longer uniform since not all sums have equal probability.

The discrete uniform distribution itself is inherently non-parametric. It is convenient, however, to represent its values generally by an integer interval [a,b], so that a,b become the main parameters of the distribution (often one simply considers the interval [1,n] with the single parameter n).

References:

Implements

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

Extension Methods