Exponential-Poisson distribution: estimation and applications to rainfall and aircraft data with zero occurrence

Abstract

In this study, different frequentist estimation procedures for the parameters of the exponential-Poisson distribution are considered, such as the maximum likelihood, method of moments, ordinary and weighted least-squares, percentile, maximum product of spacings, Cramér-von Mises and Anderson-Darling maximum goodness-of-fit estimators. We compare them using extensive numerical simulations, which show that using a nested expectation-maximization algorithm in the maximum likelihood estimators with bootstrap bias correction does not require numerical procedures to solve nonlinear equations and returns accurate parameter estimates. Finally, our proposed methodology is fully illustrated using two real data sets (rainfall and aircraft data) with the occurrence of zero values.

Keywords:

• Kus distribution; Maximum likelihood estimation; Anderson-Darling estimators; Meteorological applications; Zero occurrence

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. The research was partially supported by the Brazilian organizations, CNPq and FAPESP.

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes

1 The distribution is obtained by mixing exponential and zero-truncated Poisson distributions; see Kus (2007) for details.