Optimal record-based statistical procedures for the two-parameter exponential distribution
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.
invariant test two-parameter exponential model generalized likelihood ratio test monotone likelihood ratio neyman-pearson fundamental lemma shortest-width confidence interval uniformly most powerful test unbiased interval