Poisson.html

Poisson.java

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package blog.distrib;

import blog.*;
import java.io.Serializable;
import java.util.*;
import common.Util;

A Poisson distribution with mean and variance lambda. This is a distribution over non-negative integers. The probability of n is exp(-lambda) lambda^n / n!. This is a slightly modified version of Poisson.java in the common directory, tailored to implement the CondProbDistrib interface.


public class Poisson extends AbstractCondProbDistrib implements Serializable {

Creates a new Poisson distribution with the specifies lambda parameter.


    public Poisson(List params) {
	if (!(params.get(0) instanceof Number)) {
	    throw new IllegalArgumentException
		("The first parameter to Poisson " 
		 + "distribution must be of class Number, "
		 + "not " + params.get(0).getClass() + ".");
	}

	lambda = ((Number)params.get(0)).doubleValue() ;
    }

Returns the probability of the integer n under this distribution.


    public double getProb(List args, Object value) {
	// Work in log domain to avoid overflow for large values of n
	return Math.exp(getLogProb(args, value)); 
    }

Returns the log probability of the integer n under this distribution.


    public double getLogProb(List args, Object value) {
	int n = ((Number)value).intValue(); 
	return (-lambda + (n * Math.log(lambda)) - Util.logFactorial(n));
    }

Returns an integer sampled according to this distribution. This implementation takes time proportional to the magnitude of the integer returned. I got the algorithm from Anuj Kumar's course page for IEOR E4404 at Columbia University, specifically the file:

http://www.columbia.edu/~ak2108/ta/summer2003/poisson1.c


    public Object sampleVal(List args, Type childType) {
	int n = 0;
	double probOfN = Math.exp(-lambda); // start with prob of 0
	double cumProb = probOfN;

	double u = Util.random();
	while (cumProb < u) {
	    n++;
	    // ratio between P(n) and P(n-1) is lambda / n
	    probOfN *= (lambda / n);
	    cumProb += probOfN;
	}

	return new Integer(n);
    }

    public String toString() {
	return getClass().getName();
    }

    private double lambda;
}

This file was generated on Tue Jun 08 17:53:47 PDT 2010 from file Poisson.java
by the ilog.language.tools.Hilite Java tool written by Hassan Aït-Kaci