umontreal.iro.lecuyer.probdist
Class HypergeometricDist

java.lang.Object
  umontreal.iro.lecuyer.probdist.DiscreteDistributionInt
      umontreal.iro.lecuyer.probdist.HypergeometricDist

All Implemented Interfaces:

Distribution

public class HypergeometricDist
extends DiscreteDistributionInt

Extends the class DiscreteDistributionInt for the hypergeometric distribution 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 <= m <= l and 1 <= k <= l. Its mass function is given by

p(x) = nCr(m, x)nCr(l - m, k - x)/nCr(l, k), for max(0, k - l + m) <= x <= min(k, m),

where nCr is defined in BinomialDist.

Field Summary

static double

MAXN

Fields inherited from class umontreal.iro.lecuyer.probdist.DiscreteDistributionInt

EPSILON

Constructor Summary

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

Method Summary

double	barF(int x) Returns bar(F)(x), the complementary distribution function.
static double	barF(int m, int l, int k, int x) Computes the complementary distribution function.
double	cdf(int x) Returns the distribution function F evaluated at x (see).
static double	cdf(int m, int l, int k, int x) Computes the distribution function F(x).
int	getK() Returns the k associated with this object.
int	getL() Returns the l associated with this object.
int	getM() Returns the m associated with this object.
double	getMean() Returns the mean of the distribution function.
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.
double[]	getParams() Return a table containing the parameters of the current distribution.
double	getStandardDeviation() Returns the standard deviation of the distribution function.
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.
double	getVariance() Returns the variance of the distribution function.
static double	getVariance(int m, int l, int k) Computes and returns the variance of the hypergeometric distribution with parameters m, l and k.
static int	inverseF(int m, int l, int k, double u) Computes F-1(u) for the hypergeometric distribution without using precomputed tables.
int	inverseFInt(double u) Returns the inverse distribution function F-1(u), where 0 <= u <= 1.
double	prob(int x) Returns p(x), the probability of x.
static double	prob(int m, int l, int k, int x) Computes the hypergeometric probability p(x).
void	setParams(int m, int l, int k) Resets the parameters of this object to m, l and k.
String	toString()

Methods inherited from class umontreal.iro.lecuyer.probdist.DiscreteDistributionInt

barF, cdf, getXinf, getXsup, inverseF

Methods inherited from class java.lang.Object

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

Field Detail

MAXN

public static double MAXN

Constructor Detail

HypergeometricDist

public HypergeometricDist(int m,
                          int l,
                          int k)

Constructs an hypergeometric distribution with parameters m, l and k.

Method Detail

prob

public double prob(int x)

Description copied from class: DiscreteDistributionInt

Returns p(x), the probability of x.

Specified by:

prob in class DiscreteDistributionInt

Parameters:

x - value at which the mass function must be evaluated

Returns:

the mass function evaluated at x

cdf

public double cdf(int x)

Description copied from class: DiscreteDistributionInt

Returns the distribution function F evaluated at x (see).

Specified by:

cdf in class DiscreteDistributionInt

Parameters:

x - value at which the distribution function must be evaluated

Returns:

the distribution function evaluated at x

barF

public double barF(int x)

Description copied from class: DiscreteDistributionInt

Returns bar(F)(x), the complementary distribution function. See the WARNING above.

Overrides:

barF in class DiscreteDistributionInt

Parameters:

x - value at which the complementary distribution function must be evaluated

Returns:

the complementary distribution function evaluated at x

inverseFInt

public int inverseFInt(double u)

Description copied from class: DiscreteDistributionInt

Returns the inverse distribution function F^-1(u), where 0 <= u <= 1. The default implementation uses binary search.

Overrides:

inverseFInt in class DiscreteDistributionInt

Parameters:

u - value in the interval (0, 1) for which the inverse distribution function is evaluated

Returns:

the inverse distribution function evaluated at u

getMean

public double getMean()

Description copied from interface: Distribution

Returns the mean of the distribution function.

getVariance

public double getVariance()

Description copied from interface: Distribution

Returns the variance of the distribution function.

getStandardDeviation

public double getStandardDeviation()

Description copied from interface: Distribution

Returns the standard deviation of the distribution function.

prob

public static double prob(int m,
                          int l,
                          int k,
                          int x)

Computes the hypergeometric probability p(x).

cdf

public static double cdf(int m,
                         int l,
                         int k,
                         int x)

Computes the distribution function F(x).

barF

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

Computes the complementary distribution function. WARNING: The complementary distribution function is defined as bar(F)(x) = P[X >= x].

inverseF

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

Computes F^-1(u) for the hypergeometric distribution without using precomputed tables. The inversion is computed using the chop-down algorithm.

getMean

public 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.

Returns:

the mean of the hypergeometric distribution E[X] = km/l

getVariance

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

Computes and returns the variance of the hypergeometric distribution with parameters m, l and k.

Returns:

the variance of the Hypergeometric distribution Var[X] = (km/l )(1 - m/l )(l - k)/(l - 1)

getStandardDeviation

public 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.

Returns:

the standard deviation of the hypergeometric distribution

getM

public int getM()

Returns the m associated with this object.

getL

public int getL()

Returns the l associated with this object.

getK

public int getK()

Returns the k associated with this object.

getParams

public double[] getParams()

Return a table containing the parameters of the current distribution. This table is put in regular order: [m, l, k].

setParams

public void setParams(int m,
                      int l,
                      int k)

Resets the parameters of this object to m, l and k.

toString

public String toString()

Overrides:

toString in class Object