Bayesian inference on multiply sequential order statistics from heterogeneous exponential populations with GLR test for homogeneity

ABSTRACT

In this article, sequential order statistics (SOS) coming from heterogeneous exponential distributions are considered. Maximum likelihood and Bayesian estimates of parameters are derived on the basis of multiple SOS samples. Admissibility of the Bayes estimates are discussed and proved by the well-known Blyth’s lemma. Based on the available data, confidence intervals and highest posterior density credible sets are obtained. The generalized likelihood ratio (GLRT) and the Bayesian tests (under the “0 − K” loss function) are derived for testing homogeneity of the exponential populations. It is shown that the GLRT in this case is scale invariant. Some guidelines for deriving the uniformly most powerful scale-invariant test (if exists) are also given.

KEYWORDS:

• Admissibility
• Bayesian approach
• Estimation
• Hypothesis testing
• Invariant test
• Sequential order statistics

MATHEMATICS SUBJECT CLASSIFICATION:

• 62N05
• 62P30
• 62G30

Acknowledgments

The authors thank the editor-in-chief, the associate editor, and the anonymous reviewers for their useful comments on the earlier version of this article.