umontreal.iro.lecuyer.probdist
Class NegativeBinomialDist

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

public class NegativeBinomialDist
extends DiscreteDistributionInt

Extends the class DiscreteDistributionInt for the negative binomial distribution with parameters n and p, where n is a positive integer and 0 <= p <= 1. Its mass function is

p(x) = nCr(n + x - 1, x)pⁿ(1 - p)^x, for x = 0, 1, 2,…

where nCr is defined in BinomialDist. This p(x) can be interpreted as the probability of having x failures before the nth success in a sequence of independent Bernoulli trials with probability of success p. For n = 1, this gives the geometric distribution.

Field Summary

static double

MAXN

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

EPSILON

Constructor Summary

NegativeBinomialDist(int n, double p)
Creates an object that contains the probability terms and the distribution function for the negative binomial distribution with parameter n and p.

Method Summary

double	barF(int x) Returns bar(F)(x), the complementary distribution function.
double	cdf(int x) Returns the distribution function F evaluated at x (see).
static double	cdf(int n, double p, int x) Computes the distribution function.
int	getN() Returns the parameter n of this object.
double	getP() Returns the parameter p of this object.
int	inverseF(double u) Returns the inverse distribution function F-1(u), where 0 <= u <= 1.
static int	inverseF(int n, double p, double u) Computes the inverse function without precomputing tables.
double	prob(int x) Returns p(x), the probability of x, which should be a real number in the interval [0, 1].
static double	prob(int n, double p, int x) Computes the probability mass function.
void	setParams(int n, double p) Sets the parameter n and p of this object.

Methods inherited from class java.lang.Object

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

Field Detail

MAXN

public static double MAXN

Constructor Detail

NegativeBinomialDist

public NegativeBinomialDist(int n,
                            double p)

Creates an object that contains the probability terms and the distribution function for the negative binomial distribution with parameter n and p.

Method Detail

prob

public double prob(int x)

Description copied from class: DiscreteDistributionInt

Returns p(x), the probability of x, which should be a real number in the interval [0, 1].

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.

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

inverseF

public int inverseF(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:

inverseF 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

prob

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

Computes the probability mass function.

cdf

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

Computes the distribution function.

inverseF

public static int inverseF(int n,
                           double p,
                           double u)

Computes the inverse function without precomputing tables. This method computes the CDF at the mode (maximum term) and performs a linear search from that point.

getN

public int getN()

Returns the parameter n of this object.

getP

public double getP()

Returns the parameter p of this object.

setParams

public void setParams(int n,
                      double p)

Sets the parameter n and p of this object.