Example: Exponential Probability Distribution

This example obtains the Exponential probability density, gradient and Hessian values at a point.

import com.imsl.stat.distributions.ExponentialPD;

public class ExponentialPDEx1 {

    public static void main(String[] args) {

        double x = 2.0 / (5.0 + 1.0);
        double scale = 3.0;
        ExponentialPD epd = new ExponentialPD();

        double pdf = epd.pdf(x, scale);
        double[] gradient = epd.getPDFGradient(x, scale);
        double[][] hessian = epd.getPDFHessian(x, scale);

        System.out.printf("Probability density at %.3f with scale value of 3.0"
                + " = %.3f\n\n", x, pdf);
        System.out.printf("Probability density gradient at %.3f with scale"
                + " value of 3.0 = {%.3f}\n\n", x, gradient[0]);
        System.out.printf("Probability density Hessian at %.3f with scale"
                + " value of 3.0 = {{%.3f}}\n\n", x, hessian[0][0]);
    }
}

Output

Probability density at 0.333 with scale value of 3.0 = 1.104

Probability density gradient at 0.333 with scale value of 3.0 = {0.000}

Probability density Hessian at 0.333 with scale value of 3.0 = {{-0.123}}