Probability in the Engineering and Informational Sciences

Table of Contents - 1989 - Volume 3, Issue 03  

Articles

Crossing Properties of Mixture Distributions

Philip J. Bolanda11, Frank Proschana22 and Y. L. Tonga33

a1 Department of Statistics University College, Dublin Belfield, Dublin 4, Ireland

a2 Department of Statistics The Florida State University Tallahassee, Florida 32306-3033

a3 School of Mathematics Georgia Institute of Technology, Atlanta, Georgia 30332

Abstract

Mixture distributions are a frequently used tool in modelling random phenomena. We consider mixtures of densities from a one-parameter exponenvial family of distributions. Using the tools of totally positive functions and the variation-diminishing property of such, we study the effect of sign-crossing properties of two mixing densities μ1 and μ2 on the resulting mixture distributions f1 and f2. The results enable us to make stochastic and variability cornparisons for binomial-beta, mixed Weibull, and mixed gamma distributions.

Footnotes

1 Research partially supported by AFOSR Grant No. 88-0040.

2 Research supported by AFOSR Grant No. 88-0040.

3 Research supported by NSF Grants DMS-8502346 and DMS-8801327.