Example Normal Probability Distribution

This example evaluates the normal density, approximate gradient and hessian, and analytic gradient and hessian for a small sample of data.

import com.imsl.math.*;
import com.imsl.stat.distributions.*;
import java.text.DecimalFormat;

public class NormalPDEx1 {

    public static void main(String[] args) throws Exception {
        double x[] = {
            24.67074744935116, 23.452437146719504, 23.508058666655124,
            24.085805009837582, 26.387706562892493, 26.244756646592872
        };

        double[] values = new double[x.length];
        double mean = 25.0;
        double stdDev = 1.0;

        NormalPD normal = new NormalPD();

        for (int i = 0; i < x.length; i++) {
            values[i] = normal.pdf(x[i], mean, stdDev);
        }

        PrintMatrixFormat pmf = new PrintMatrixFormat();
        pmf.setNumberFormat(new DecimalFormat("0.00000000"));

        PrintMatrix pm = new PrintMatrix("Normal(25.0,1.0) pdf values at x=");
        pm.print(x);

        pm.setTitle("f(x;a,b)=");
        pm.print(values);

        double[] gradientApprox
                = normal.getPDFGradientApproximation(x[0], mean, stdDev);

        pm.setTitle("Gradient approximation f(x;a,b) at x[0]");
        pm.print(gradientApprox);

        double[] gradient = normal.getPDFGradient(x[0], mean, stdDev);

        pm.setTitle("Gradient f(x;a,b) at x[0]");
        pm.print(gradient);

        double[][] hessianApprox
                = normal.getPDFHessianApproximation(x[0], mean, stdDev);

        pm.setTitle("Hessian approximation of f(x;a,b) at x[0]");
        pm.print(pmf, hessianApprox);

        double[][] hessian = normal.getPDFHessian(x[0], mean, stdDev);

        pm.setTitle("Hessian of f(x;a,b) at x[0]");
        pm.print(pmf, hessian);
    }
}

Output

Normal(25.0,1.0) pdf values at x=
     0     
0  24.671  
1  23.452  
2  23.508  
3  24.086  
4  26.388  
5  26.245  

f(x;a,b)=
     0    
0  0.378  
1  0.12   
2  0.131  
3  0.263  
4  0.152  
5  0.184  

Gradient approximation f(x;a,b) at x[0]
     0     
0  -0.124  
1  -0.337  

Gradient f(x;a,b) at x[0]
     0     
0  -0.124  
1  -0.337  

Hessian approximation of f(x;a,b) at x[0]
        0           1       
0  -0.33692738  0.35977953  
1   0.35977953  0.55539644  

Hessian of f(x;a,b) at x[0]
        0           1       
0  -0.33692735  0.35977916  
1   0.35977916  0.55539649