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package jhplot.math.num.pdf;

import jhplot.math.num.Constants;
import jhplot.math.num.NumericException;

/**
 * 

 * The Poisson distribution.
 * 
 * 

 * References:
 * 

 * 
 Eric W. Weisstein. "Poisson Distribution." From MathWorld--A Wolfram Web
 * Resource. 
 * http://mathworld.wolfram.com/Poisson.html 
 * 
 * 

 * 
 * @since 1.2
 * @version $Revision: 1.3 $ $Date: 2007/11/18 23:51:21 $
 */
public class Poisson extends DiscreteDistribution {

    /** the mean. */
    private double mean;

    /**
     * Default distribution. The means is set to one.
     */
    public Poisson() {
        this(1.0);
    }

    /**
     * Create a distribution with the given mean.
     * 
     * @param m the mean.
     */
    public Poisson(double m) {
        super();
        setMean(m);
    }

    /**
     * The CDF for this distribution. This method returns P(X ≤ x).
     * 
     * @param x the value at which the CDF is evaluated.
     * @return CDF for this distribution.
     * @throws NumericException if the cumulative probability can not be
     *         computed.
     */
    public double cumulativeProbability(int x) throws NumericException {
        double ret;

        if (x < 0) {
            ret = 0.0;
        } else {
            ret = simpleCumulativeProbability(0, x);
        }

        return ret;
    }

    /**
     * The inverse CDF for this distribution. This method returns the largest x
     * such that, P(X ≤ x) ≤ p. The return value must also satisfy P(X
     * ≥ x) &ge 1 - p.
     * 
     * @param p the cumulative probability.
     * @return x
     * @throws NumericException if the inverse cumulative probability can not be
     *         computed.
     */
    public int inverseCumulativeProbability(double p) throws NumericException {
        int ret;

        if (p < 0.0 || p > 1.0 || Double.isNaN(p)) {
            ret = Integer.MIN_VALUE;
        } else if (p == 0.0) {
            ret = -1;
        } else if (p == 1.0) {
            ret = Integer.MAX_VALUE;
        } else {
            ret = findInverseCumulativeProbability(p, 0, (int) (mean + 0.5),
                Integer.MAX_VALUE);
        }

        return ret;
    }

    /**
     * The PMF for this distribution. This method returns P(X = x).
     * 
     * @param x the value at which the probability is evaluated.
     * @return PMF for this distribution.
     */
    public double probability(int x) {
        double ret;
        if (x < 0) {
            ret = 0.0;
        } else if (x == 0) {
            ret = Math.exp(-mean);
        } else {
            ret = Math.exp(-SaddlePoint.getStirlingError(x)
                - SaddlePoint.getDeviancePart(x, mean))
                / Math.sqrt(Constants.PI_2 * x);
        }
        return ret;
    }

    /**
     * Access the mean.
     * 
     * @return the mean.
     */
    public double getMean() {
        return mean;
    }

    /**
     * Modify the mean.
     * 
     * @param m the new mean value.
     */
    public void setMean(double m) {
        if (Double.isNaN(m) || m <= 0.0) {
            throw new IllegalArgumentException("mean must be positive.");
        }
        this.mean = m;
    }
}