Extends the class DiscreteDistributionInt for the hypergeometric distribution [66] (page 101) with \(k\) elements chosen among \(l\), \(m\) being of one type, and \(l-m\) of the other. More...

Inheritance diagram for HypergeometricDist:

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Collaboration diagram for HypergeometricDist:

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Public Member Functions
	HypergeometricDist (int m, int l, int k)
	Constructs an hypergeometric distribution with parameters \(m\), \(l\) and \(k\).

double	prob (int x)

double	cdf (int x)

double	barF (int x)

int	inverseFInt (double u)

double	getMean ()
	Returns the mean of the distribution function.

double	getVariance ()
	Returns the variance of the distribution function.

double	getStandardDeviation ()
	Returns the standard deviation of the distribution function.

int	getM ()
	Returns the \(m\) associated with this object.

int	getL ()
	Returns the \(l\) associated with this object.

int	getK ()
	Returns the \(k\) associated with this object.

double []	getParams ()
	Return a table containing the parameters of the current distribution. More...

void	setParams (int m, int l, int k)
	Resets the parameters of this object to \(m\), \(l\) and \(k\).

String	toString ()
	Returns a `String` containing information about the current distribution.

Public Member Functions inherited from DiscreteDistributionInt
abstract double	prob (int x)
	Returns \(p(x)\), the probability of \(x\). More...

double	cdf (double x)
	Returns the distribution function \(F\) evaluated at \(x\) (see ( FDistDisc )). More...

abstract double	cdf (int x)
	Returns the distribution function \(F\) evaluated at \(x\) (see ( FDistDisc )). More...

double	barF (double x)
	Returns \(\bar{F}(x)\), the complementary distribution function. More...

double	barF (int x)
	Returns \(\bar{F}(x)\), the complementary distribution function. More...

int	getXinf ()
	Returns the lower limit \(x_a\) of the support of the probability mass function. More...

int	getXsup ()
	Returns the upper limit \(x_b\) of the support of the probability mass function. More...

double	inverseF (double u)
	Returns the inverse distribution function \(F^{-1}(u)\), where. More...

int	inverseFInt (double u)
	Returns the inverse distribution function \(F^{-1}(u)\), where. More...

Static Public Member Functions
static double	prob (int m, int l, int k, int x)
	Computes the hypergeometric probability \(p(x)\) given by ( fheperg ).

static double	cdf (int m, int l, int k, int x)
	Computes the distribution function \(F(x)\).

static double	barF (int m, int l, int k, int x)
	Computes the complementary distribution function. More...

static int	inverseF (int m, int l, int k, double u)
	Computes \(F^{-1}(u)\) for the hypergeometric distribution without using precomputed tables. More...

static double	getMean (int m, int l, int k)
	Computes and returns the mean \(E[X] = km/l\) of the Hypergeometric distribution with parameters \(m\), \(l\) and \(k\). More...

static double	getVariance (int m, int l, int k)
	Computes and returns the variance \(\mbox{Var}[X] = \frac{(km/l)(1 - m/l)(l - k)}{l - 1}\) of the hypergeometric distribution with parameters \(m\), \(l\) and \(k\). More...

static double	getStandardDeviation (int m, int l, int k)
	Computes and returns the standard deviation of the hypergeometric distribution with parameters \(m\), \(l\) and \(k\). More...

Static Public Attributes
Constant
static double	MAXN = 100000
	If the number of integers in the interval \([\max(0,k-l+m), \min(k,m)]\) is larger than this constant, the tables will not be precomputed by the constructor.

Static Public Attributes inherited from DiscreteDistributionInt
static double	EPSILON = 1.0e-16
	Environment variable that determines what probability terms can be considered as negligible when building precomputed tables for distribution and mass functions. More...

Additional Inherited Members
Protected Attributes inherited from DiscreteDistributionInt
double	cdf [] = null

double	pdf [] = null

int	xmin = 0

int	xmax = 0

int	xmed = 0

int	supportA = Integer.MIN_VALUE

int	supportB = Integer.MAX_VALUE

Static Protected Attributes inherited from DiscreteDistributionInt
static final double	EPS_EXTRA = 1.0e-6

Detailed Description

Extends the class DiscreteDistributionInt for the hypergeometric distribution [66] (page 101) with \(k\) elements chosen among \(l\), \(m\) being of one type, and \(l-m\) of the other.

The parameters \(m\), \(k\) and \(l\) are positive integers where \(1\le m\le l\) and \(1\le k\le l\). Its mass function is given by

\[ p(x) = \frac{ \binom{m}{x} \binom{l - m}{k-x}}{\binom{l}{k}} \qquad\mbox{for } \max(0,k-l+m)\le x\le\min(k, m). \tag{fheperg} \]

Member Function Documentation

◆ barF()

static double barF	(	int	m,
		int	l,
		int	k,
		int	x
	)

static

Computes the complementary distribution function.

WARNING: The complementary distribution function is defined as \(\bar{F}(x) = P[X \ge x]\).

◆ getMean()

static double getMean	(	int	m,
		int	l,
		int	k
	)

static

Computes and returns the mean \(E[X] = km/l\) of the Hypergeometric distribution with parameters \(m\), \(l\) and \(k\).

Returns: the mean of the hypergeometric distribution \(E[X] = km / l\)

◆ getParams()

double [] getParams ( )

Return a table containing the parameters of the current distribution.

This table is put in regular order: [ \(m\), \(l\), \(k\)].

Implements Distribution.

◆ getStandardDeviation()

static double getStandardDeviation	(	int	m,
		int	l,
		int	k
	)

static

Computes and returns the standard deviation of the hypergeometric distribution with parameters \(m\), \(l\) and \(k\).

Returns: the standard deviation of the hypergeometric distribution

◆ getVariance()

static double getVariance	(	int	m,
		int	l,
		int	k
	)

static

Computes and returns the variance \(\mbox{Var}[X] = \frac{(km/l)(1 - m/l)(l - k)}{l - 1}\) of the hypergeometric distribution with parameters \(m\), \(l\) and \(k\).

Returns: the variance of the Hypergeometric distribution \(\mbox{Var}[X] = (km / l)(1 - m / l)(l - k) / (l - 1)\)

◆ inverseF()

static int inverseF	(	int	m,
		int	l,
		int	k,
		double	u
	)

static

Computes \(F^{-1}(u)\) for the hypergeometric distribution without using precomputed tables.

The inversion is computed using the chop-down algorithm [102] .

The documentation for this class was generated from the following file:

HypergeometricDist.java

Public Member Functions

Static Public Member Functions

Static Public Attributes

Additional Inherited Members

Detailed Description

Member Function Documentation

◆ barF()

◆ getMean()

◆ getParams()

◆ getStandardDeviation()

◆ getVariance()

◆ inverseF()