On the likelihood estimation of the parameters of Gompertz distribution based on complete and progressively Type-II censored samples

Abstract

In this paper, by considering a progressively Type-II censored sample from the two-parameter Gompertz distribution, a necessary and sufficient condition is established for the existence and uniqueness of the maximum-likelihood estimates of the shape and scale parameters. The results for the special cases of complete and ordinary Type-II right censored samples are then deduced. Several numerical examples from the literature are presented for the purpose of illustrating the established results.

Keywords:

• Gompertz distribution
• maximum-likelihood estimates
• existence and uniqueness
• ordinary Type-II right censoring
• progressive Type-II censoring

Acknowledgements

The authors express their sincere thanks to the reviewer and the associate editor for making some useful suggestions on an earlier version of this manuscript which resulted in this improved version.