com.datumbox.framework.core.statistics.distributions

Class ContinuousDistributions

java.lang.Object

com.datumbox.framework.core.statistics.distributions.ContinuousDistributions

public class ContinuousDistributions
extends java.lang.Object

This class provides methods for the CDFs and PDFs of the most common continuous distributions.

Constructor Summary

Constructors

Constructor and Description
ContinuousDistributions()

Method Summary

Modifier and Type	Method and Description
static double	betaCdf(double x, double a, double b) Calculates the probability from 0 to X under Beta Distribution
static double	chisquareCdf(double x, int df) Returns the probability from 0 to x of a specific chisquare score and degrees of freedom
static double	chisquareInverseCdf(double p, int df) Returns the x score of a specific pvalue and degrees of freedom for Chisquare.
static double	dirichletPdf(double[] pi, double a) Implementation for single alpha value.
static double	dirichletPdf(double[] pi, double[] ai) Calculates probability pi, ai under dirichlet distribution
static double	exponentialCdf(double x, double lamda) Calculates the probability from 0 to X under Exponential Distribution
static double	fCdf(double x, int f1, int f2) Calculates the probability from 0 to X under F Distribution
static double	gamma(double x) It estimates a numeric approximation of gamma function.
static double	gammaCdf(double x, double a, double b) Calculates the probability from 0 to X under Gamma Distribution
static double	gaussCdf(double z) Returns the p-value of a specific z score for Gaussian Ported from C# code posted at http://jamesmccaffrey.wordpress.com/2010/11/05/programmatically-computing-the-area-under-the-normal-curve/
static double	gaussInverseCdf(double p) Returns the z score of a specific pvalue for Gaussian Partially ported from http://home.online.no/~pjacklam/notes/invnorm/impl/karimov/StatUtil.java Other implementations http://home.online.no/~pjacklam/notes/invnorm/index.html#Java
static double	kolmogorov(double z) Returns the cumulative probability of kolmogorov
static double	logGamma(double Z) Log Gamma Function
static double	multinomialGaussianPdf(double[] mean, double[][] covariance, double[] x) Calculates the PDF of Multinomial Normal Distribution for a particular x.
static double[]	multinomialGaussianSample(double[] mean, double[][] covariance) Samples from Multinomial Normal Distribution.
static double	normalQuantile(double p, double mu, double sigma) Compute the quantile function for the normal distribution.
static double	studentsCdf(double x, int df) Calculates the probability from -INF to X under Student's Distribution Ported to PHP from Javascript implementation found at http://www.math.ucla.edu/~tom/distributions/tDist.html
static double	uniformCdf(double x, double a, double b) Returns the cumulative probability of Uniform

Methods inherited from class java.lang.Object

equals, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Constructor Detail

ContinuousDistributions

public ContinuousDistributions()

Method Detail

chisquareCdf

public static double chisquareCdf(double x,
                                  int df)

Returns the probability from 0 to x of a specific chisquare score and degrees of freedom

Parameters:

x -

df -

Returns:

gaussCdf

public static double gaussCdf(double z)

Returns the p-value of a specific z score for Gaussian Ported from C# code posted at http://jamesmccaffrey.wordpress.com/2010/11/05/programmatically-computing-the-area-under-the-normal-curve/

Parameters:

z -

Returns:

gamma

public static double gamma(double x)

It estimates a numeric approximation of gamma function.

Parameters:

x - The input x

Returns:

The value of gamma(x)

logGamma

public static double logGamma(double Z)

Log Gamma Function

Parameters:

Z -

Returns:

studentsCdf

public static double studentsCdf(double x,
                                 int df)

Calculates the probability from -INF to X under Student's Distribution Ported to PHP from Javascript implementation found at http://www.math.ucla.edu/~tom/distributions/tDist.html

Parameters:

x -

df -

Returns:

exponentialCdf

public static double exponentialCdf(double x,
                                    double lamda)

Calculates the probability from 0 to X under Exponential Distribution

Parameters:

x -

lamda -

Returns:

betaCdf

public static double betaCdf(double x,
                             double a,
                             double b)

Calculates the probability from 0 to X under Beta Distribution

Parameters:

x -

a -

b -

Returns:

fCdf

public static double fCdf(double x,
                          int f1,
                          int f2)

Calculates the probability from 0 to X under F Distribution

Parameters:

x -

f1 -

f2 -

Returns:

gammaCdf

public static double gammaCdf(double x,
                              double a,
                              double b)

Calculates the probability from 0 to X under Gamma Distribution

Parameters:

x -

a -

b -

Returns:

uniformCdf

public static double uniformCdf(double x,
                                double a,
                                double b)

Returns the cumulative probability of Uniform

Parameters:

x -

a -

b -

Returns:

kolmogorov

public static double kolmogorov(double z)

Returns the cumulative probability of kolmogorov

Parameters:

z -

Returns:

gaussInverseCdf

public static double gaussInverseCdf(double p)

Returns the z score of a specific pvalue for Gaussian Partially ported from http://home.online.no/~pjacklam/notes/invnorm/impl/karimov/StatUtil.java Other implementations http://home.online.no/~pjacklam/notes/invnorm/index.html#Java

Parameters:

p -

Returns:

chisquareInverseCdf

public static double chisquareInverseCdf(double p,
                                         int df)

Returns the x score of a specific pvalue and degrees of freedom for Chisquare. It We just do a bisectionsearch for a value within CHI_EPSILON, relying on the monotonicity of chisquareCdf(). Ported from Javascript code posted at http://www.fourmilab.ch/rpkp/experiments/analysis/chiCalc.js

Parameters:

p -

df -

Returns:

normalQuantile

public static double normalQuantile(double p,
                                    double mu,
                                    double sigma)

Compute the quantile function for the normal distribution. For small to moderate probabilities, algorithm referenced below is used to obtain an initial approximation which is polished with a final Newton step. For very large arguments, an algorithm of Wichura is used. Used by ShapiroWilk Test Ported by Javascript implementation found at https://raw.github.com/rniwa/js-shapiro-wilk/master/shapiro-wilk.js Originally ported from http://svn.r-project.org/R/trunk/src/nmath/qnorm.c

Parameters:

p -

mu -

sigma -

Returns:

dirichletPdf

public static double dirichletPdf(double[] pi,
                                  double[] ai)

Calculates probability pi, ai under dirichlet distribution

Parameters:

pi - The vector with probabilities.

ai - The vector with pseudocounts.

Returns:

The probability

dirichletPdf

public static double dirichletPdf(double[] pi,
                                  double a)

Implementation for single alpha value.

Parameters:

pi - The vector with probabilities.

a - The alpha parameter for all pseudocounts.

Returns:

The probability

multinomialGaussianSample

public static double[] multinomialGaussianSample(double[] mean,
                                                 double[][] covariance)

Samples from Multinomial Normal Distribution.

Parameters:

mean -

covariance -

Returns:

A multinomialGaussianSample from the Multinomial Normal Distribution

multinomialGaussianPdf

public static double multinomialGaussianPdf(double[] mean,
                                            double[][] covariance,
                                            double[] x)

Calculates the PDF of Multinomial Normal Distribution for a particular x.

Parameters:

mean -

covariance -

x - The x record

Returns:

The multinomialGaussianPdf of x