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package jhplot.math.num.pdf;


/**
 * 

 * The Rayleigh distribution.
 * 
 * 

 * References:
 * 

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

 * 
 * @since 1.2
 * @version $Revision: 1.2 $ $Date: 2007/10/25 04:44:10 $
 */
public class Rayleigh extends ContinuousDistribution {

    /** the scale parameter. */
    private double scale;

    /**
     * Default constructor. The scale parameter is set to one.
     */
    public Rayleigh() {
        this(1.0);
    }

    /**
     * Create a distribution with the scale parameter.
     * 
     * @param s the scale parameter.
     */
    public Rayleigh(double s) {
        super();
        setScale(s);
    }

    /**
     * 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.
     */
    public double cumulativeProbability(double x) {
        double ret;

        if (Double.isNaN(x)) {
            ret = Double.NaN;
        } else if (x <= 0.0) {
            ret = 0.0;
        } else if (Double.isInfinite(x)) {
            ret = 1.0;
        } else {
            double r = x / scale;
            ret = 1.0 - Math.exp(-r * r / 2.0);
        }

        return ret;
    }

    /**
     * Access the scale parameter.
     * 
     * @return the scale parameter.
     */
    public double getScale() {
        return scale;
    }

    /**
     * The inverse CDF for this distribution. This method returns x such that,
     * P(X < x) = p.
     * 
     * @param p the cumulative probability.
     * @return x
     */
    public double inverseCumulativeProbability(double p) {
        double ret;

        if (p < 0.0 || p > 1.0 || Double.isNaN(p)) {
            ret = Double.NaN;
        } else if (p == 0.0) {
            ret = 0.0;
        } else if (p == 1.0) {
            ret = Double.POSITIVE_INFINITY;
        } else {
            double q = 1.0 - p;
            ret = scale * Math.sqrt(Math.log(1.0 / (q * q)));
        }

        return ret;
    }

    /**
     * Modify the scale parameter.
     * 
     * @param s The new scale parameter value.
     */
    public void setScale(double s) {
        if (s <= 0.0 || Double.isNaN(s)) {
            throw new IllegalArgumentException(
                "scale parameter must be positive.");
        }
        this.scale = s;
    }
}