edu.uah.math.distributions
Class Functions

java.lang.Object
  edu.uah.math.distributions.Functions

public final class Functions
extends java.lang.Object

This class defines a collection of static functions that are useful in probability.

Version:

August, 2003

Author:

Kyle Siegrist, Dawn Duehring

Field Summary

static double	EULER
static int	WITH_REPLACEMENT
static int	WITHOUT_REPLACEMENT

Constructor Summary

Functions()

Method Summary

static double	beta(double a, double b) This method returns an approximation to the beta function.
static double	betaCDF(double x, double a, double b) The method computes the beta cumulative distribution function.
static double	comb(double n, int k) This method computes the number of combinations of a specified number of objects chosen from a population of a specified size.
static double	factorial(int k) This method computes the factorial function, the number of permutations of a specified number of objects.
static double	gamma(double x) This method computes the gamma function.
static double	gammaCDF(double x, double a) This method computes the cumulative distribution function of the gamma distribution with a specified shape parameter and scale parameter 1.
static int	getIndex(int i, int n) This method returns an index between 0 and n - 1, for use in error correcting in arrays.
static double[]	getProbabilities(double[] a) This method takes an array of numbers and returns a probability array (nonnegatie numbers that sum to 1).
static double	getProbability(double p) This method takes a real number and converts it to a probability (a number between 0 and 1).
static int[]	getSample(int[] p, int n, int t) This method computes a sample of a specified size from a specified population and of a specified type (with or without replacement).
static int[]	getSample(int m, int n, int t) This method computes a sample of a specified size from a population of the form 1, 2, ..., m
static boolean	isReal(double x) This class method tests to see if a specified number is real.
static double	logGamma(double x) This method computes the log of the gamma function.
static double	perm(double n, int k) This method computes the number of permuatations of a specified number of objects chosen from a population of a specified number of objects.
static double[]	sort(double[] a) This method sorts an array of doubles.
static int[]	sort(int[] a) This method sorts an array of integers.

Methods inherited from class java.lang.Object

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

Field Detail

WITHOUT_REPLACEMENT

public static final int WITHOUT_REPLACEMENT

See Also:

Constant Field Values

WITH_REPLACEMENT

public static final int WITH_REPLACEMENT

See Also:

Constant Field Values

EULER

public static final double EULER

See Also:

Constant Field Values

Constructor Detail

Functions

public Functions()

Method Detail

getProbabilities

public static double[] getProbabilities(double[] a)

This method takes an array of numbers and returns a probability array (nonnegatie numbers that sum to 1). Negative numbers in the original array are converted to zeros, and the remaining numbers scaled by the sum of the numbers, assuming that not all of the original numbers are 0. In the last case, the method returns the uniform probabiltiy array.

Parameters:

a - the array of numbers

Returns:

the probability array

getProbability

public static double getProbability(double p)

This method takes a real number and converts it to a probability (a number between 0 and 1).

Parameters:

p - the given number

Returns:

the probability.

getIndex

public static int getIndex(int i,
                           int n)

This method returns an index between 0 and n - 1, for use in error correcting in arrays.

Parameters:

i - the given index

n - the specified size of the array

Returns:

the verified index between 0 and n - 1

perm

public static double perm(double n,
                          int k)

This method computes the number of permuatations of a specified number of objects chosen from a population of a specified number of objects.

Parameters:

n - the population size

k - the sample size

Returns:

the number of ordered samples

factorial

public static double factorial(int k)

This method computes the factorial function, the number of permutations of a specified number of objects.

Parameters:

k - the number of objects

Returns:

the number of permutations of the objects

comb

public static double comb(double n,
                          int k)

This method computes the number of combinations of a specified number of objects chosen from a population of a specified size.

Parameters:

n - the population size

k - the sample size

Returns:

the number of unordered samples

logGamma

public static double logGamma(double x)

This method computes the log of the gamma function.

Parameters:

x - a positive number

Returns:

the log of the gamma function at x

gamma

public static double gamma(double x)

This method computes the gamma function.

Parameters:

x - a positive number

Returns:

the gamma function at x

gammaCDF

public static double gammaCDF(double x,
                              double a)

This method computes the cumulative distribution function of the gamma distribution with a specified shape parameter and scale parameter 1.

Parameters:

x - a positive number

a - the shape parameter

Returns:

the cumulative probability at x

betaCDF

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

The method computes the beta cumulative distribution function.

Parameters:

x - a number between 0 and 1

a - the left paramter

b - the right parameter

Returns:

the beta cumulative probability at x

beta

public static double beta(double a,
                          double b)

This method returns an approximation to the beta function.

Parameters:

a - the left value

b - the right value

Returns:

the beta function at (a, b)

getSample

public static int[] getSample(int[] p,
                              int n,
                              int t)

This method computes a sample of a specified size from a specified population and of a specified type (with or without replacement).

Parameters:

p - the population

n - the sample size

t - the type (0 without replacement, 1 with replacemen);

getSample

public static int[] getSample(int m,
                              int n,
                              int t)

This method computes a sample of a specified size from a population of the form 1, 2, ..., m

Parameters:

m - the population size

n - the sample size

t - the type (0 without replacement, 1 with replacement)

sort

public static double[] sort(double[] a)

This method sorts an array of doubles.

Parameters:

a - the array of doubles

Returns:

the sorted arry

sort

public static int[] sort(int[] a)

This method sorts an array of integers.

Parameters:

a - the array of integers

Returns:

the sorted arry

isReal

public static boolean isReal(double x)

This class method tests to see if a specified number is real.

Parameters:

x - the number

Returns:

true if the number is real and finite