This example obtains maximum likelihood estimates for the parameters of a beta distribution.
import com.imsl.math.*; import com.imsl.stat.distributions.*; import java.text.DecimalFormat; public class MaximumLikelihoodEstimationEx1 { public static void main(String[] args) throws Exception { double[] x = { 0.12396e0, 0.58037e0, 0.28837e0, 0.38195e0, 0.44387e0, 0.17680e0, 0.22661e0, 0.55939e0, 0.41646e0, 0.33781e0, 0.63768e0, 0.81501e0, 0.55952e0, 0.50559e0, 0.39315e0, 0.67901e0, 0.66032e0, 0.52279e0, 0.53164e0, 0.19165e0, 0.83432e0, 0.16578e0, 0.30614e0, 0.57622e0, 0.24793e0, 0.55212e0, 0.32037e0, 0.62443e0, 0.54663e0, 0.56399e0, 0.61369e0, 0.62853e0, 0.47957e0, 0.57208e0, 0.44813e0, 0.69026e0, 0.73784e0, 0.28413e0, 0.18926e0, 0.58319e0, 0.28740e0, 0.61739e0, 0.32052e0, 0.29761e0, 0.68279e0, 0.75275e0, 0.48364e0, 0.56711e0, 0.72584e0, 0.32971e0, 0.86950e0, 0.79991e0, 0.52609e0, 0.46006e0, 0.52828e0, 0.27842e0, 0.58179e0, 0.37934e0, 0.29819e0, 0.53552e0, 0.46476e0, 0.22105e0, 0.36031e0, 0.49400e0, 0.41216e0, 0.34985e0, 0.26751e0, 0.57636e0, 0.54788e0, 0.48447e0, 0.75758e0, 0.60260e0, 0.56603e0, 0.57345e0, 0.35777e0, 0.79578e0, 0.46025e0, 0.57042e0, 0.31177e0, 0.56309e0, 0.52548e0, 0.69891e0, 0.27270e0, 0.38819e0, 0.73049e0, 0.54734e0, 0.50803e0, 0.48510e0, 0.87042e0, 0.52287e0, 0.67998e0, 0.40186e0, 0.48845e0, 0.64425e0, 0.65228e0, 0.45132e0, 0.23021e0, 0.39449e0, 0.70417e0, 0.31853e0 }; BetaPD beta = new BetaPD(); MaximumLikelihoodEstimation mle = new MaximumLikelihoodEstimation(x, beta, 1, 1); mle.compute(); double[] parameterEstimates = mle.getEstimates(); double[][] hessian = mle.getHessian(); double[] stdErrs = mle.getStandardErrors(); double mLogLikelihood = mle.getMinusLogLikelihood(); PrintMatrixFormat pmf = new PrintMatrixFormat(); pmf.setNumberFormat(new DecimalFormat("0.00000000")); PrintMatrix pm = new PrintMatrix("MLEs"); pm.print(pmf, parameterEstimates); pm.setTitle("hessian"); pm.print(pmf, hessian); pm.setTitle("standard errors"); pm.print(pmf, stdErrs); System.out.printf("Minus log likelihood: %5.2f\n", mLogLikelihood); } }
MLEs 0 0 3.67112042 1 3.73274034 hessian 0 1 0 -16.82252107 14.45938489 1 14.45938489 -16.23511103 standard errors 0 0 0.50349626 1 0.51252395 Minus log likelihood: -35.22Link to Java source.