On estimation of parameters of the exponential power family of distributions

Abstract

Consider the three-parameter exponential power distribution with location parameter μ, scale parameter σ² and shape (power) parameter β. This is a general symmetric family of distributions with normal, double exponential and rectangular as special cases. Such distributions are used in Bayesian statistics as a wider choice of symmetric parent distribution and in classical statistics in determination of lack of normality. This note obtains simultaneous estimates of μ, σ² and β by method of moments and method of maximum likelihood. It also studies the behavior of estimates of β through Monte Carlo simulation when values of μ and σ² are set equal to zero and unity respectively.

Keywords:

• Central moments
• kurtosis
• heuristic estimates
• robust ordered linear unbiased minimum variance estimates
• bisection method