Crossing Properties of Mixture Distributions
Philip J. Boland, Frank Proschan, Y. L. Tong · Probability in the Engineering and Informational Sciences · 1989
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 μ1and μ2on the resulting mixture distributionsf1andf2. The results enable us to make stochastic and variability cornparisons for binomial-beta, mixed Weibull, and mixed gamma distributions.