SSJ
V. 2.6.

umontreal.iro.lecuyer.probdist
Class PascalDist

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

SSJ
V. 2.6.

To submit a bug or ask questions, send an e-mail to Pierre L'Ecuyer.