java.lang.Object
- org.mariuszgromada.math.mxparser.mathcollection.ProbabilityDistributions

```
public final class ProbabilityDistributions
extends Object
```
ProbabilityDistributions - random number generators, PDF - Probability Distribution Functions, CDF - Cumulative Distribution Functions, QNT - Quantile Functions (Inverse Cumulative Distribution Functions).

Version:

5.2.0

Author:

Mariusz Gromada
MathParser.org - mXparser project page
mXparser on GitHub
INFIMA place to purchase a commercial MathParser.org-mXparser software license
info@mathparser.org
ScalarMath.org - a powerful math engine and math scripting language
Scalar Lite
Scalar Pro
MathSpace.pl

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Field Summary

Fields
Modifier and Type Field Description

static Random randomGenerator
Random number generator

Constructor Summary

Constructors
Constructor Description

ProbabilityDistributions()

Method Summary

All Methods Static Methods Concrete Methods
Modifier and Type	Method	Description
`static double`	`cdfChiSquared(double x, double k)`	Cumulative distribution function - Chi-Squared distribution
`static double`	`cdfNormal(double x, double mean, double stddev)`	CDF - Cumulative Distribution Function - Normal distribution N(mean, stddev).
`static double`	`cdfSnedecordF(double x, double d1, double d2)`	Cumulative distribution function - Snedecor's F distribution (F-distribution or F-ratio, also known as Fisher–Snedecor distribution)
`static double`	`cdfStudentT(double x, double v)`	Cumulative distribution function - Student's t-distribution
`static double`	`cdfUniformContinuous(double x, double a, double b)`	CDF - Cumulative Distribution Function - Uniform Continuous distribution over interval [a, b).
`static double`	`getRandomVariableValue(int randomVariableId)`	Returns random variable value, where random variable is represented by the token id in the RandomVariable class
`static double`	`pdfChiSquared(double x, double k)`	Probability distribution function - Chi-Squared distribution
`static double`	`pdfNormal(double x, double mean, double stddev)`	PDF - Probability Distribution Function - Normal distribution N(mean, stddev).
`static double`	`pdfSnedecordF(double x, double d1, double d2)`	Probability distribution function - Snedecor's F distribution (F-distribution or F-ratio, also known as Fisher–Snedecor distribution)
`static double`	`pdfStudentT(double x, double v)`	Probability distribution function - Student's t-distribution
`static double`	`pdfUniformContinuous(double x, double a, double b)`	PDF - Probability Distribution Function - Uniform Continuous distribution over interval [a, b).
`static double`	`qntChiSquared(double p, double k)`	Quantile function (Inverse cumulative distribution function) - Chi-Squared distribution
`static double`	`qntNormal(double q, double mean, double stddev)`	QNT - Quantile Function - Normal distribution N(mean, stddev).
`static double`	`qntSnedecordF(double p, double d1, double d2)`	Quantile function (Inverse cumulative distribution function) - Snedecor's F distribution (F-distribution or F-ratio, also known as Fisher–Snedecor distribution)
`static double`	`qntStudentT(double p, double v)`	Quantile function (Inverse cumulative distribution function) - Student's t-distribution
`static double`	`qntUniformContinuous(double q, double a, double b)`	QNT - Quantile Function - Uniform Continuous distribution over interval [a, b).
`static double`	`randomUniformContinuous()`	Random number from Uniform Continuous distribution over interval [0, 1).
`static double`	`rndChiSquared(double k)`	Pseudo-random number from Chi-Squared distribution
`static int`	`rndIndex(int n)`	Random index from 0 to n-1,
`static int`	`rndIndex(int n, Random rnd)`	Random index from 0 to n-1,
`static int`	`rndInteger()`	Random integer.
`static double`	`rndInteger(double a, double b, Random rnd)`	Random number from Uniform Discrete distribution.
`static double`	`rndInteger(int a, int b)`	Random number from Uniform Discrete distribution.
`static double`	`rndInteger(int a, int b, Random rnd)`	Random number from Uniform Discrete distribution.
`static int`	`rndInteger(Random rnd)`	Random integer.
`static double`	`rndNormal(double mean, double stddev)`	Random number from normal distribution N(mean, stddev).
`static double`	`rndNormal(double mean, double stddev, Random rnd)`	Random number from normal distribution N(mean, stddev).
`static double`	`rndSnedecordF(double d1, double d2)`	Pseudo-random number from Snedecor's F distribution (F-distribution or F-ratio, also known as Fisher–Snedecor distribution)
`static double`	`rndStudentT(double v)`	Pseudo-random number from Student's t-distribution
`static double`	`rndUniformContinuous(double a, double b)`	Random number from dUniform Continuous distribution over interval [a, b).
`static double`	`rndUniformContinuous(double a, double b, Random rnd)`	Random number from Uniform Continuous distribution over interval [a, b).
`static double`	`rndUniformContinuous(Random rnd)`	Random number from Uniform Continuous distribution over interval [0, 1).

Methods inherited from class java.lang.Object
clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

- Field Detail
  - randomGenerator
```
public static Random randomGenerator
```
    Random number generator
- Constructor Detail
  - ProbabilityDistributions
```
public ProbabilityDistributions()
```
- Method Detail
  - rndUniformContinuous
```
public static double rndUniformContinuous(double a,
                                          double b,
                                          Random rnd)
```
    Random number from Uniform Continuous distribution over interval [a, b).
    
    Parameters:
    
    a - Interval limit - left / lower.
    
    b - Interval limit - right / upper.
    
    rnd - Random number generator.
    
    Returns:
    
    Double.NaN if a or b is null, or b is lower than a - otherwise returns random number.
  - rndUniformContinuous
```
public static double rndUniformContinuous(double a,
                                          double b)
```
    Random number from dUniform Continuous distribution over interval [a, b).
    
    Parameters:
    
    a - Interval limit - left / lower.
    
    b - Interval limit - right / upper.
    
    Returns:
    
    Double.NaN if a or b is null, or b is lower than a - otherwise returns random number.
  - rndUniformContinuous
```
public static double rndUniformContinuous(Random rnd)
```
    Random number from Uniform Continuous distribution over interval [0, 1).
    
    Parameters:
    
    rnd - Random number generator.
    
    Returns:
    
    Random number.
  - randomUniformContinuous
```
public static double randomUniformContinuous()
```
    Random number from Uniform Continuous distribution over interval [0, 1).
    
    Returns:
    
    Random number.
  - pdfUniformContinuous
```
public static double pdfUniformContinuous(double x,
                                          double a,
                                          double b)
```
    PDF - Probability Distribution Function - Uniform Continuous distribution over interval [a, b).
    
    Parameters:
    
    x - Point to evaluate pdf function.
    
    a - Interval limit - left / lower.
    
    b - Interval limit - right / upper.
    
    Returns:
    
    Double.NaN if a or b is null, or b is lower than a - otherwise function value.
  - cdfUniformContinuous
```
public static double cdfUniformContinuous(double x,
                                          double a,
                                          double b)
```
    CDF - Cumulative Distribution Function - Uniform Continuous distribution over interval [a, b).
    
    Parameters:
    
    x - Point to evaluate cdf function.
    
    a - Interval limit - left / lower.
    
    b - Interval limit - right / upper.
    
    Returns:
    
    Double.NaN if a or b is null, or b is lower than a - otherwise function value.
  - qntUniformContinuous
```
public static double qntUniformContinuous(double q,
                                          double a,
                                          double b)
```
    QNT - Quantile Function - Uniform Continuous distribution over interval [a, b). (Inverse of Cumulative Distribution Function).
    
    Parameters:
    
    q - Quantile.
    
    a - Interval limit - left / lower.
    
    b - Interval limit - right / upper.
    
    Returns:
    
    Double.NaN if a or b is null, or b is lower than a or q is lower than 0 or q is greater than 1 - otherwise function value.
  - rndInteger
```
public static double rndInteger(int a,
                                int b,
                                Random rnd)
```
    Random number from Uniform Discrete distribution. over set interval (a, a+1, ..., b-1, b).
    
    Parameters:
    
    a - Interval limit - left / lower.
    
    b - Interval limit - right / upper.
    
    rnd - Random number generator.
    
    Returns:
    
    Double.NaN if a or b is null, or b is lower than a - otherwise returns random number.
  - rndInteger
```
public static double rndInteger(double a,
                                double b,
                                Random rnd)
```
    Random number from Uniform Discrete distribution. over set interval (a, a+1, ..., b-1, b).
    
    Parameters:
    
    a - Interval limit - left / lower.
    
    b - Interval limit - right / upper.
    
    rnd - Random number generator.
    
    Returns:
    
    Double.NaN if a or b is null, or b is lower than a - otherwise returns random number.
  - rndInteger
```
public static double rndInteger(int a,
                                int b)
```
    Random number from Uniform Discrete distribution. over set interval (a, a+1, ..., b-1, b).
    
    Parameters:
    
    a - Interval limit - left / lower.
    
    b - Interval limit - right / upper.
    
    Returns:
    
    Double.NaN if a or b is null, or b is lower than a - otherwise returns random number.
  - rndInteger
```
public static int rndInteger(Random rnd)
```
    Random integer.
    
    Parameters:
    
    rnd - Random number generator.
    
    Returns:
    
    Returns random number.
  - rndIndex
```
public static int rndIndex(int n,
                           Random rnd)
```
    Random index from 0 to n-1,
    
    Parameters:
    
    n - Bound.
    
    rnd - Random number generator.
    
    Returns:
    
    if n < 0 returns -1, otherwise random index.
  - rndIndex
```
public static int rndIndex(int n)
```
    Random index from 0 to n-1,
    
    Parameters:
    
    n - Bound.
    
    Returns:
    
    if n < 0 returns -1, otherwise random index.
  - rndInteger
```
public static int rndInteger()
```
    Random integer.
    
    Returns:
    
    Double.NaN if a or b is null, or b is lower than a - otherwise returns random number.
  - rndNormal
```
public static double rndNormal(double mean,
                               double stddev,
                               Random rnd)
```
    Random number from normal distribution N(mean, stddev).
    
    Parameters:
    
    mean - Mean value.
    
    stddev - Standard deviation.
    
    rnd - Random number generator.
    
    Returns:
    
    Double.NaN if mean or stddev or rnd is null or stddev is lower than 0 - otherwise random number.
  - rndNormal
```
public static double rndNormal(double mean,
                               double stddev)
```
    Random number from normal distribution N(mean, stddev).
    
    Parameters:
    
    mean - Mean value.
    
    stddev - Standard deviation.
    
    Returns:
    
    Double.NaN if mean or stddev is null or stddev is lower than 0 - otherwise random number.
  - pdfNormal
```
public static double pdfNormal(double x,
                               double mean,
                               double stddev)
```
    PDF - Probability Distribution Function - Normal distribution N(mean, stddev).
    
    Parameters:
    
    x - Point to evaluate pdf function.
    
    mean - Mean value.
    
    stddev - Standard deviation.
    
    Returns:
    
    Double.NaN if mean or stddev is null or stddev is lower than 0 - otherwise function value.
  - cdfNormal
```
public static double cdfNormal(double x,
                               double mean,
                               double stddev)
```
    CDF - Cumulative Distribution Function - Normal distribution N(mean, stddev).
    
    Parameters:
    
    x - Point to evaluate pdf function.
    
    mean - Mean value.
    
    stddev - Standard deviation.
    
    Returns:
    
    Double.NaN if mean or stddev is null or stddev is lower than 0 - otherwise function value.
  - qntNormal
```
public static double qntNormal(double q,
                               double mean,
                               double stddev)
```
    QNT - Quantile Function - Normal distribution N(mean, stddev). (Inverse of Cumulative Distribution Function).
    
    Parameters:
    
    q - Quantile.
    
    mean - Mean value.
    
    stddev - Standard deviation.
    
    Returns:
    
    Double.NaN if mean or stddev is null or stddev is lower than 0 or q is lower than 0 or q is greater than 1 - otherwise function value.
  - pdfStudentT
```
public static double pdfStudentT(double x,
                                 double v)
```
    Probability distribution function - Student's t-distribution
    
    Parameters:
    
    x - Given point.
    
    v - Number of degrees of freedom.
    
    Returns:
    
    Returns the PDF of Student's t-distribution.
  - cdfStudentT
```
public static double cdfStudentT(double x,
                                 double v)
```
    Cumulative distribution function - Student's t-distribution
    
    Parameters:
    
    x - Given point.
    
    v - Number of degrees of freedom.
    
    Returns:
    
    Returns the CDF of Student's t-distribution.
  - qntStudentT
```
public static double qntStudentT(double p,
                                 double v)
```
    Quantile function (Inverse cumulative distribution function) - Student's t-distribution
    
    Parameters:
    
    p - Probability
    
    v - Number of degrees of freedom.
    
    Returns:
    
    Returns the quantile of Student's t-distribution
  - rndStudentT
```
public static double rndStudentT(double v)
```
    Pseudo-random number from Student's t-distribution
    
    Parameters:
    
    v - Number of degrees of freedom.
    
    Returns:
    
    returns Pseudo-random number from Student's t-distribution
  - pdfChiSquared
```
public static double pdfChiSquared(double x,
                                   double k)
```
    Probability distribution function - Chi-Squared distribution
    
    Parameters:
    
    x - Given point.
    
    k - Number of degrees of freedom.
    
    Returns:
    
    Returns the PDF of Chi-Squared t-distribution.
  - cdfChiSquared
```
public static double cdfChiSquared(double x,
                                   double k)
```
    Cumulative distribution function - Chi-Squared distribution
    
    Parameters:
    
    x - Given point.
    
    k - Number of degrees of freedom.
    
    Returns:
    
    Returns the CDF of Chi-Squared distribution.
  - qntChiSquared
```
public static double qntChiSquared(double p,
                                   double k)
```
    Quantile function (Inverse cumulative distribution function) - Chi-Squared distribution
    
    Parameters:
    
    p - Probability
    
    k - Number of degrees of freedom.
    
    Returns:
    
    Returns the quantile of Chi-Squared distribution
  - rndChiSquared
```
public static double rndChiSquared(double k)
```
    Pseudo-random number from Chi-Squared distribution
    
    Parameters:
    
    k - Number of degrees of freedom.
    
    Returns:
    
    returns Pseudo-random number from Chi-Squared distribution
  - pdfSnedecordF
```
public static double pdfSnedecordF(double x,
                                   double d1,
                                   double d2)
```
    Probability distribution function - Snedecor's F distribution (F-distribution or F-ratio, also known as Fisher–Snedecor distribution)
    
    Parameters:
    
    x - Real value
    
    d1 - Number of degrees of freedom - 1
    
    d2 - Number of degrees of freedom - 2
    
    Returns:
    
    Returns the PDF of Snedecor's F distribution (F-distribution or F-ratio, also known as Fisher–Snedecor distribution)
  - cdfSnedecordF
```
public static double cdfSnedecordF(double x,
                                   double d1,
                                   double d2)
```
    Cumulative distribution function - Snedecor's F distribution (F-distribution or F-ratio, also known as Fisher–Snedecor distribution)
    
    Parameters:
    
    x - Real value
    
    d1 - Number of degrees of freedom - 1
    
    d2 - Number of degrees of freedom - 2
    
    Returns:
    
    Returns the CDF of Snedecor's F distribution (F-distribution or F-ratio, also known as Fisher–Snedecor distribution)
  - qntSnedecordF
```
public static double qntSnedecordF(double p,
                                   double d1,
                                   double d2)
```
    Quantile function (Inverse cumulative distribution function) - Snedecor's F distribution (F-distribution or F-ratio, also known as Fisher–Snedecor distribution)
    
    Parameters:
    
    p - Probability
    
    d1 - Number of degrees of freedom - 1
    
    d2 - Number of degrees of freedom - 2
    
    Returns:
    
    Returns the quantile of Snedecor's F distribution (F-distribution or F-ratio, also known as Fisher–Snedecor distribution)
  - rndSnedecordF
```
public static double rndSnedecordF(double d1,
                                   double d2)
```
    Pseudo-random number from Snedecor's F distribution (F-distribution or F-ratio, also known as Fisher–Snedecor distribution)
    
    Parameters:
    
    d1 - Number of degrees of freedom - 1
    
    d2 - Number of degrees of freedom - 2
    
    Returns:
    
    Returns Pseudo-random number from Snedecor's F distribution (F-distribution or F-ratio, also known as Fisher–Snedecor distribution)
  - getRandomVariableValue
```
public static double getRandomVariableValue(int randomVariableId)
```
    Returns random variable value, where random variable is represented by the token id in the RandomVariable class
    
    Parameters:
    
    randomVariableId - Please refer to RandomVariable class.
    
    Returns:
    
    Returns random variable value if id is known, otherwise Double.NaN is returned.
    
    See Also:
    
    RandomVariable

Class ProbabilityDistributions

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Field Summary

Constructor Summary

Method Summary

Methods inherited from class java.lang.Object

Field Detail

randomGenerator

Constructor Detail

ProbabilityDistributions

Method Detail

rndUniformContinuous

rndUniformContinuous

rndUniformContinuous

randomUniformContinuous

pdfUniformContinuous

cdfUniformContinuous

qntUniformContinuous

rndInteger

rndInteger

rndInteger

rndInteger

rndIndex

rndIndex

rndInteger

rndNormal

rndNormal

pdfNormal

cdfNormal

qntNormal

pdfStudentT

cdfStudentT

qntStudentT

rndStudentT

pdfChiSquared

cdfChiSquared

qntChiSquared

rndChiSquared

pdfSnedecordF

cdfSnedecordF

qntSnedecordF

rndSnedecordF

getRandomVariableValue