Package edu.cmu.tetrad.util

Class ProbUtils

java.lang.Object

edu.cmu.tetrad.util.ProbUtils

public class ProbUtils
extends Object

Implements a number of important functions from probability and statistics.> 0

We don't know who wrote this class; we didn't. All we added was the documentation. -Joe Ramsey, jdramsey@andrew.cmu.edu> 0

Version:

$Id: $Id

Author:

Unknown, but thanks

Method Summary

Modifier and Type	Method	Description
static int	bernoulliRand(double p)	bernoulliRand.
static double	betaCdf(double x, double pin, double qin)	Incomplete Beta function.
static double	betaPdf(double x, double a, double b)	betaPdf.
static double	betaQuantile(double alpha, double p, double q)	betaQuantile.
static double	betaRand(double a, double b)	Beta distribution random generator.
static double	binomialCdf(int k, int n, double p)	Binomial cumulative distribution function.
static double	binomialPmf(int k, int n, double p)	binomialPmf.
static int	binomialQuantile(double x, int n, double p)	binomialQuantile.
static int	binomialRand(int n, double pp)	Binomial random generator from Numerical Recipes
static double	biNormalCdf(double ah, double ak, double r)	Bivariate normal CDF.
static double	cauchyCdf(double x)	Cauchy CDF
static double	cauchyPdf(double x)	cauchyPdf.
static double	cauchyQuantile(double x)	cauchyQuantile.
static double	cauchyRand()	Cauchy random generator.
static double	chisqCdf(double x, double df)	chisqCdf.
static double	chisqPdf(double x, double v)	chisqPdf.
static double	chisqQuantile(double p, double v)	chisqQuantile.
static double	chisqRand(double df)	Chi square random generator.
static double	fCdf(double x, double df1, double df2)	F CDF.
static double	fPdf(double x, double a, double b)	fPdf.
static double	fQuantile(double p, double df1, double df2)	fQuantile.
static double	fRand(double ndf, double ddf)	F distribution random generator.
static double	gammaCdf(double a, double x)	compute complementary gamma cdf by its continued fraction expansion
static double	gammaPdf(double x, double a)	gammaPdf.
static double	gammaQuantile(double a, double p)	gammaQuantile.
static double	gammaRand(double a)	Gamma random generator.
static double	lngamma(double xx)	This is a more literal (that is, exact) copy of the log gamma method from Numerical Recipes than the following one.
static double	logbeta(double p, double q)	Calculates the log beta function of p and q.
static double	multinormalProb(double[] a, double[] b, double[][] cov)	Compute the probability over a rectangular region with correlation matrix c.
static double	normalCdf(double y)	Normal cumulative distribution function (the value which results by integrating the normal distribution function from negative infinity up to y).
static double	normalPdf(double x)	normalPdf.
static double	normalQuantile(double p)	normalQuantile.
static double	normalRand()	Normal random generator
static double	poissonCdf(int k, double y)	poissonCdf.
static double	poissonPmf(int k, double lambda)	poissonPmf.
static int	poissonQuantile(double x, double l)	poissonQuantile.
static int	poissonRand(double xm)	Poisson random generator from Numerical Recipes
static double	tCdf(double x, double df)	CACM Algorithm 395, by G.
static double	tPdf(double x, double a)	tPdf.
static double	tQuantile(double pp, double n)	CACM Algorithm 396, by G.
static double	tRand(double df)	T distribution random generator.
static double	uniformRand()	uniformRand.
static void	uniformSeeds(long a, long b)	uniformSeeds.

Methods inherited from class java.lang.Object

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

Method Details

normalCdf

public static double normalCdf(double y)

Normal cumulative distribution function (the value which results by integrating the normal distribution function from negative infinity up to y).

Parameters:

y - the upper limit of integration.

Returns:

the area accumulated in the integration.

lngamma

public static double lngamma(double xx)

This is a more literal (that is, exact) copy of the log gamma method from Numerical Recipes than the following one. It was created by cutting and pasting from the PDF version of the book and then converting C syntax to Java. The static double array above goes with this. Converted to Java by Frank Wimberly

Parameters:

xx - a double

Returns:

the value ln[?(xx)] for xx > 0

logbeta

public static double logbeta(double p,
 double q)

Calculates the log beta function of p and q.

Parameters:

p - a double

q - a double

Returns:

a double

betaCdf

public static double betaCdf(double x,
 double pin,
 double qin)

Incomplete Beta function. Translated from FORTRAN july 1977 edition. w. fullerton, c3, los alamos scientific lab. based on bosten and battiste, remark on algorithm 179, comm. acm, v 17, p 153, (1974).

Parameters:

x - upper limit of integration. x must be in (0,1) inclusive.

pin - first beta distribution parameter. p must be gt 0.0.

qin - second beta distribution parameter. q must be gt 0.0.

Returns:

result.

binomialCdf

public static double binomialCdf(int k,
 int n,
 double p)

Binomial cumulative distribution function.

Parameters:

k - a int

n - a int

p - a double

Returns:

a double

cauchyCdf

public static double cauchyCdf(double x)

Cauchy CDF

Parameters:

x - a double

Returns:

a double

fCdf

public static double fCdf(double x,
 double df1,
 double df2)

F CDF.

Parameters:

x - a double

df1 - a double

df2 - a double

Returns:

a double

gammaCdf

public static double gammaCdf(double a,
 double x)

compute complementary gamma cdf by its continued fraction expansion

Parameters:

a - a double

x - a double

Returns:

a double

chisqCdf

public static double chisqCdf(double x,
 double df)

chisqCdf.

Parameters:

x - a double

df - a double

Returns:

a double

poissonCdf

public static double poissonCdf(int k,
 double y)

poissonCdf.

Parameters:

k - a int

y - a double

Returns:

a double

tCdf

public static double tCdf(double x,
 double df)

CACM Algorithm 395, by G. W. Hill

Parameters:

x - a double

df - a double

Returns:

a double

betaQuantile

public static double betaQuantile(double alpha,
 double p,
 double q)

betaQuantile.

Parameters:

alpha - a double

p - a double

q - a double

Returns:

a double

binomialQuantile

public static int binomialQuantile(double x,
 int n,
 double p)

binomialQuantile.

Parameters:

x - a double

n - a int

p - a double

Returns:

a int

cauchyQuantile

public static double cauchyQuantile(double x)

cauchyQuantile.

Parameters:

x - a double

Returns:

a double

chisqQuantile

public static double chisqQuantile(double p,
 double v)

chisqQuantile.

Parameters:

p - a double

v - a double

Returns:

a double

fQuantile

public static double fQuantile(double p,
 double df1,
 double df2)

fQuantile.

Parameters:

p - a double

df1 - a double

df2 - a double

Returns:

a double

gammaQuantile

public static double gammaQuantile(double a,
 double p)

gammaQuantile.

Parameters:

a - a double

p - a double

Returns:

a double

normalQuantile

public static double normalQuantile(double p)

normalQuantile.

Parameters:

p - a double

Returns:

a double

poissonQuantile

public static int poissonQuantile(double x,
 double l)

poissonQuantile.

Parameters:

x - a double

l - a double

Returns:

a int

tQuantile

public static double tQuantile(double pp,
 double n)

CACM Algorithm 396, by G. W. Hill

Parameters:

pp - a double

n - a double

Returns:

a double

betaPdf

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

betaPdf.

Parameters:

x - a double

a - a double

b - a double

Returns:

a double

binomialPmf

public static double binomialPmf(int k,
 int n,
 double p)

binomialPmf.

Parameters:

k - a int

n - a int

p - a double

Returns:

a double

cauchyPdf

public static double cauchyPdf(double x)

cauchyPdf.

Parameters:

x - a double

Returns:

a double

chisqPdf

public static double chisqPdf(double x,
 double v)

chisqPdf.

Parameters:

x - a double

v - a double

Returns:

a double

fPdf

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

fPdf.

Parameters:

x - a double

a - a double

b - a double

Returns:

a double

gammaPdf

public static double gammaPdf(double x,
 double a)

gammaPdf.

Parameters:

x - a double

a - a double

Returns:

a double

normalPdf

public static double normalPdf(double x)

normalPdf.

Parameters:

x - a double

Returns:

a double

poissonPmf

public static double poissonPmf(int k,
 double lambda)

poissonPmf.

Parameters:

k - a int

lambda - a double

Returns:

a double

tPdf

public static double tPdf(double x,
 double a)

tPdf.

Parameters:

x - a double

a - a double

Returns:

a double

uniformSeeds

public static void uniformSeeds(long a,
 long b)

uniformSeeds.

Parameters:

a - a long

b - a long

uniformRand

public static double uniformRand()

uniformRand.

Returns:

a double

bernoulliRand

public static int bernoulliRand(double p)

bernoulliRand.

Parameters:

p - a double

Returns:

a int

poissonRand

public static int poissonRand(double xm)

Poisson random generator from Numerical Recipes

Parameters:

xm - a double

Returns:

a int

binomialRand

public static int binomialRand(int n,
 double pp)

Binomial random generator from Numerical Recipes

Parameters:

n - a int

pp - a double

Returns:

a int

normalRand

public static double normalRand()

Normal random generator

Returns:

a double

cauchyRand

public static double cauchyRand()

Cauchy random generator.

Returns:

a double

gammaRand

public static double gammaRand(double a)

Gamma random generator.

Parameters:

a - a double

Returns:

a double

chisqRand

public static double chisqRand(double df)

Chi square random generator.

Parameters:

df - a double

Returns:

a double

tRand

public static double tRand(double df)

T distribution random generator.

Parameters:

df - a double

Returns:

a double

betaRand

public static double betaRand(double a,
 double b)

Beta distribution random generator.

Parameters:

a - a double

b - a double

Returns:

a double

fRand

public static double fRand(double ndf,
 double ddf)

F distribution random generator.

Parameters:

ndf - a double

ddf - a double

Returns:

a double

biNormalCdf

public static double biNormalCdf(double ah,
 double ak,
 double r)

Bivariate normal CDF. Adapted from statlib, file general/gaut.c, by Ajay Shah. Adaptation for Java found here --November 1st 2003, Ricardo Silva

Parameters:

ah - upper bound 1

ak - upper bound 1

r - correlatiohn

Returns:

a double

multinormalProb

public static double multinormalProb(double[] a,
 double[] b,
 double[][] cov)

Compute the probability over a rectangular region with correlation matrix c. Algorithm extracted from Alan Genz: Numerical Computation of Multivariate Normal Probabilities; revised version published in J. Comp. Graph Stat. 1 (1992), pp. 141-149. http://www.math.wsu.edu/faculty/genz/homepage Warning: this method has the side effect of changing the order of the elements in the arrays given as input. --November 3st 2003, Ricardo Silva

Parameters:

a - lower bounds (use Double.NEGATIVE_INFINITY if necessary)

b - upper bounds (use Double.POSITIVE_INFINITY if necessary)

cov - an array of objects

Returns:

a double