AISM 53, 620-630

© 2001 ISM

## 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 $X_1, \ldots, X_n$ given
$(\Theta_1,\ldots,\Theta_n)$, 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 (*DTP*), dependence by reverse regular (*DRR*), $MTP_2$ dependence, associated random variables, concomitants of order statistics
and record values, frailty models.

**Source**
(TeX , DVI )