DEPENDENCE PROPERTIES OF MULTIVARIATE MIXTURE DISTRIBUTIONS AND THEIR APPLICATIONS

BAHA-ELDIN KHALEDI AND SUBHASH KOCHAR

Stat-Math Unit, Indian Statistical Institute 7, SJS Sansanwal Marg New Delhi-110016, India, e-mail: kochar@isid.ac.in

(Received September 6, 1999; revised February 7, 2000)

Abstract. Consider a multivariate mixture model where the random variables X_{1}, …, X_{n} given (Θ_{1}, …, Θ_{n}), are conditionally independent. Conditions are obtained under which different kinds of positive dependence hold among X_{i}’s. The results obtained are applied to a variety of problems including the concomitants of order statistics and of record values; and to frailty models.

Key words and phrases: Dependence by total positivity (DT P), dependence by reverse regular (DRR), MT P_{2} dependence, associated random variables, concomitants of order statistics and record values, frailty models.