Abstract

In this paper we study some methods to reduce the bias for maximum likelihood estimation in the general class of alpha power models, specifically for the shape parameter. We find the modified maximum likelihood estimator using Firth’s method and we show that this estimator is the uniformly minimum variance unbiased estimator (UMVUE) in this class. We consider three special cases of this class, namely the exponentiated exponential (EE), the power half-normal and the power piecewise exponential models. We compare the bias in simulation studies and find that the modified method is definitely superior, especially for small sample sizes, in both the bias and the root mean squared error. We illustrate our modified estimator in four real data set examples, in each of which the modified estimates better explain the variability.