Discrete Weibull distribution: different estimation methods under ranked set sampling and simple random sampling

Abstract

The discrete Weibull (DW) is a discretized version of the well-known Weibull distribution, and, as such can be considered in reliability and survival analyses where the variable of interest involves some kind of count. Furthermore, since the DW distribution can account for both under and overdispersion, it is an alternative to the orthodox Poisson distribution. The main objective of this study is to evaluate the performance of nine different estimation methods, applied to DW distribution, under simple random sampling (SRS) and ranked set sampling (RSS). A comprehensive simulation study was presented for this purpose, including additional simulation based on real data sets. A parametric bootstrap approach was also developed to provide confidence intervals based on RSS samples. The results allowed us to quantify the superiority of RSS over SRS, and provided important insights about the efficiency of the estimation methods when the counts are under or overdispersed.

Keywords:

• Hellinger distance
• imperfect ranking
• maximum-likelihood estimation
• minimum discrepancy methods
• parametric bootstrap
• relative efficiency

Acknowledgement

We thank the associate editor and the anonymous reviewers for their constructive comments, which helped us to improve the manuscript.

Disclosure statement

No potential conflict of interest was reported by the author(s).