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Crossing Properties of Mixture Distributions

Published online by Cambridge University Press:  27 July 2009

Philip J. Boland ,
Frank Proschan  and
Y. L. Tong
Philip J. Boland
Affiliation:
Department of Statistics University College, Dublin Belfield, Dublin 4, Ireland
Frank Proschan
Affiliation:
Department of StatisticsThe Florida State University Tallahassee, Florida 32306-3033
Y. L. Tong
Affiliation:
School of MathematicsGeorgia Institute of Technology, Atlanta, Georgia 30332
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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.

Type
Articles
Information
Probability in the Engineering and Informational Sciences , Volume 3 , Issue 3 , July 1989 , pp. 355 - 366
Copyright
Copyright © Cambridge University Press 1989

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