Umpu Tests for Testing Symmetry and Stress-Passing in Some Bivariate Exponential Models

Abstract

Bivariate exponential distributions (BVEDs) were introduced by Freund (1961). MarshallOlkin (1967), Block-Basu (1974) and Proschan-Sullo (1974) as models for the distributions of (X _l, X ₂), the failure times of dependent components (C ₁, C ₂). In this paper, we study the structure of two sub-models of Freund (1961) and Proschan-Sullo (1974) which are called stress-passing models and increased (decreased) stress models. We obtain MLEs and their asymptotic multivariate normal (AMVN) distribution. We develop uniformly most powerful unbiased (UMPU) tests based on complete samples for testing symmetry as well as stress passing in these BVED models. We show that the stress-passing models also satisfy loss of memory property (LMP).

Keywords:

• AMS Classification
• 62F03

Keywords:

• Bivariate exponential model
• Freund model
• generalized likelihood ratio test
• increased (Decreased) stress model
• loss of memory property
• Proschan-Sullo model
• simultaneous failures
• stress-passing model
• symmetry
• UMPU test