Stochastic Ordering of Exponential Family Distributions and Their Mixturesxk

By Yaming Yu. Journal of Applied Probability, 2009

47 citations recorded by the source corpus.

We investigate stochastic comparisons between exponential family distributions and their mixtures with respect to the usual stochastic order, the hazard rate order, the reversed hazard rate order, and the likelihood ratio order. A general theorem based on the notion of relative log-concavity is shown to unify various specific results for the Poisson, binomial, negative binomial, and gamma distributions in recent literature. By expressing a convolution of gamma distributions with arbitrary scale and shape parameters as a scale mixture of gamma distributions, we obtain comparison theorems concerning such convolutions that generalize some known results. Analogous results on convolutions of negative binomial distributions are also discussed.

Subfields: Applied Mathematics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/819f739a6d37b2bff77fba097ba67ff1d1c27ad8

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In Applied Mathematics

In Statistics and Probability

Citations in the corpus

Theory and inference for a class of nonlinear models with application to time series of counts (2016, background): “From Definition 2 in Yu (2009), Y ′ is log concave relative to Y ′′, Y ′ ≤lc Y ′′. As A(η) is increasing in η, limy↓0 l(y) = A(η′′)−A(η′) ≥ 0 for continuous p(y|η), and p(0|η′)/p(0|η′′) ≥ 1 for discrete p(y|η). Hence, according to Theorem 1 in Yu (2009), Y ′ is stochastically smaller than Y ′′, Y ′ ”
Theory and Inference for a Class of Observation-driven Models with Application to Time Series of Counts (2012, background): “So it follows from Definition 2 in Yu (2009) that Y ′ is log concave relative to Y ′′, i.e., Y ′ ≤lc Y ′′.”