Optimal record-based statistical procedures for the two-parameter exponential distribution

Abstract

There are a number of situations in which the experimental data observed are record statistics. In this paper, optimal confidence intervals as well as uniformly most powerful (MP) tests for one-sided alternatives are developed. Since a uniformly MP test for a two-sided alternative does not exist, generalized likelihood ratio and uniformly unbiased and invariant tests are derived for the two parameters of the exponential distribution based on record data. For illustrative purposes, a data set on the times between consecutive telephone calls to a company's switchboard is analysed using the proposed procedures. Finally, some open problems in this direction are pointed out.

Keywords:

• two-parameter exponential model
• generalized likelihood ratio test
• invariant test
• monotone likelihood ratio
• Neyman–Pearson fundamental lemma
• shortest-width confidence interval
• uniformly most powerful test
• unbiased interval

Acknowledgements

The authors are grateful to anonymous referees and the associate editor for their useful suggestions and comments on an earlier version of this paper, which resulted in this improved version of the manuscript. Doostparast's research was supported by a grant from Ferdowsi University of Mashhad (No. MS88122DSP) and Iran National Science Foundation (INSF), while the work of Balakrishnan was supported by the Natural Sciences and Engineering Research Council of Canada.