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
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.
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.