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package jhplot.math.num.pdf;

import jhplot.math.num.NumericException;

/**
 * Base discrete distribution.
 * 
 * @since 1.2
 * @version $Revision: 1.2 $ $Date: 2007/10/25 04:44:10 $
 */
public abstract class DiscreteDistribution implements Distribution {

    /**
     * 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 abstract double cumulativeProbability(int x) throws NumericException;

    /**
     * Generic means to compute cumulative probability values. This method uses
     * simple summation of the probability values to find CDF values.
     * 
     * @param x0 the lower bound of summation.
     * @param x1 the upper bound of summation.
     * @return P(x0 ≤ X ≤ x1)
     * @throws NumericException if the cumulative probability can not be
     *         computed.
     */
    protected double simpleCumulativeProbability(int x0, int x1)
        throws NumericException {
        double p = 0.0;
        for (int x = x0; x <= x1; ++x) {
            p += probability(x);
        }
        return p;
    }

    /**
     * Generic means to compute inverse cumulative probability values. This
     * method uses the bisection method to find inverse CDF values.
     * 
     * @param p the cumulative probability.
     * @param lower the global lower bound of the inverse CDF value.
     * @param initial an initial guess at the inverse CDF value.
     * @param upper the global upper bound of the inverse CDF value.
     * @return x such that P(X ≤ x) = p
     * @throws NumericException if the inverse cumulative probability can not be
     *         computed.
     */
    protected int findInverseCumulativeProbability(final double p, int lower,
        int initial, int upper) throws NumericException {
        int x = initial;
        double p0 = cumulativeProbability(x);
        while (p0 <= p && x < upper) {
            ++x;
            p0 = cumulativeProbability(x);
        }
        while (p0 > p && x >= lower) {
            --x;
            p0 = cumulativeProbability(x);
        }
        return x;
    }

    /**
     * The inverse CDF for this distribution. This method returns the largest x
     * such that, P(X ≤ x) ≤ p.
     * 
     * @param p the cumulative probability.
     * @return x
     * @throws NumericException if the inverse cumulative probability can not be
     *         computed.
     */
    public abstract int inverseCumulativeProbability(double p)
        throws NumericException;

    /**
     * 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.
     * @throws NumericException if the probability can not be computed.
     */
    public abstract double probability(int x) throws NumericException;
}