umontreal.iro.lecuyer.probdist
Class PascalDist

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

All Implemented Interfaces:

Distribution

public class PascalDist
extends NegativeBinomialDist

The Pascal distribution is a special case of 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

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

MAXN

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

EPSILON

Constructor Summary

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

Method Summary

static PascalDist	getInstanceFromMLE(int[] x, int m) Creates a new instance of a Pascal distribution with parameters n and p estimated using the maximum likelihood method based on the m observations x[i], i = 0, 1,…, m - 1.
static double[]	getMLE(int[] x, int m) Estimates the parameter (n, p) of the Pascal distribution using the maximum likelihood method, from the m observations x[i], i = 0, 1,…, m - 1.
int	getN1() Returns the parameter n of this object.
void	setParams(int n, double p) Sets the parameter n and p of this object.
String	toString()

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

barF, barF, cdf, cdf, getGamma, getInstanceFromMLE, getInstanceFromMLE1, getMean, getMean, getMLE, getMLE1, getMLEninv, getN, getP, getParams, getStandardDeviation, getStandardDeviation, getVariance, getVariance, inverseF, inverseFInt, prob, prob, setParams

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

Constructor Detail

PascalDist

public PascalDist(int n,
                  double p)

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

Method Detail

getMLE

public static double[] getMLE(int[] x,
                              int m)

Estimates the parameter (n, p) of the Pascal distribution using the maximum likelihood method, from the m observations x[i], i = 0, 1,…, m - 1. The estimates are returned in a two-element array, in regular order: [n, p].

Parameters:

x - the list of observations used to evaluate parameters

m - the number of observations used to evaluate parameters

Returns:

returns the parameters [hat(n), hat(p)]

getInstanceFromMLE

public static PascalDist getInstanceFromMLE(int[] x,
                                            int m)

Creates a new instance of a Pascal distribution with parameters n and p estimated using the maximum likelihood method based on the m observations x[i], i = 0, 1,…, m - 1.

Parameters:

x - the list of observations to use to evaluate parameters

m - the number of observations to use to evaluate parameters

getN1

public int getN1()

Returns the parameter n of this object.

setParams

public void setParams(int n,
                      double p)

Sets the parameter n and p of this object.

toString

public String toString()

Overrides:

toString in class NegativeBinomialDist