Poisson–exponential distribution: different methods of estimation

ABSTRACT

In this study, we present different estimation procedures for the parameters of the Poisson–exponential distribution, such as the maximum likelihood, method of moments, modified moments, ordinary and weighted least-squares, percentile, maximum product of spacings, Cramer–von Mises and the Anderson–Darling maximum goodness-of-fit estimators and compare them using extensive numerical simulations. We showed that the Anderson–Darling estimator is the most efficient for estimating the parameters of the proposed distribution. Our proposed methodology was also illustrated in three real data sets related to the minimum, average and the maximum flows during October at São Carlos River in Brazil demonstrating that the PE distribution is a simple alternative to be used in hydrological applications.

KEYWORDS:

• Poisson–exponential distribution
• maximum likelihood estimation
• Anderson–Darling estimators
• right-tail Anderson–Darling estimators
• hydrological applications

Acknowledgements

The authors are thankful to the Editorial Board and to the reviewers for their valuable comments and suggestions which led to this improved version.

Disclosure statement

No potential conflict of interest was reported by the authors.

ORCID

Pedro Luiz Ramos  http://orcid.org/0000-0002-5387-2457