Comparisons of ten estimation methods for the parameters of Marshall–Olkin extended exponential distribution

ABSTRACT

The aim of this article is to compare via Monte Carlo simulations the finite sample properties of the parameter estimates of the Marshall–Olkin extended exponential distribution obtained by ten estimation methods: maximum likelihood, modified moments, L-moments, maximum product of spacings, ordinary least-squares, weighted least-squares, percentile, Crámer–von-Mises, Anderson–Darling, and Right-tail Anderson–Darling. The bias, root mean-squared error, absolute and maximum absolute difference between the true and estimated distribution functions are used as criterion of comparison. The simulation study reveals that the L-moments and maximum products of spacings methods are highly competitive with the maximum likelihood method in small as well as in large-sized samples.

KEYWORDS:

• Marshall–Olkin extended family of distributions
• Monte Carlo simulations
• Parametric estimation
• Survival analysis

MATHEMATICS SUBJECT CLASSIFICATION:

• 62N02
• 62F10

Acknowledgments

We are grateful to the referees for helpful comments which improved an earlier version of the work.