Lifetime Distributions, Optimization Methods for
Kevin Hayes, Don Barry · Wiley StatsRef: Statistics Reference Online · 2014
Abstract This article introduces the likelihood function as the main tool for parameter estimation and statistical inference with lifetime distributions. When the likelihood function cannot be maximized directly, numerical optimization is required. Approaches based on the Newton–Raphson algorithm are discussed and modifications used to ensure properties such as convergence to maxima rather than minima or saddle points, calculation of nonnegative parameter estimates, and invertibility of the Fisher information matrix are considered. The variability of parameter estimates, generalized linear models, and stochastic search routines are also briefly mentioned.