Stochastic Ordering of Exponential Family Distributions and Their Mixtures

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

On the Explanatory Value of Inequity Aversion Theory

In a number of papers on their theory of Inequity Aversion, E. Fehr and K. Schmidt have claimed that the theory explains the behavior in many experiments. By virtue of having an infinite number of parameters the theory can predict a wide range of outcomes, from the competitive to the cooperative. Its prediction depends on values of these parameters. Fehr & Schmidt provide no explicit methodological plan for their project and as a result they repeatedly make logical and methodological errors. We look at the methodology of their explanations and find that no connection has been established between the experimental data and the behavior predicted by the theory. We conclude that the theory of inequity aversion has no explanatory value beyond its trivial capacity to predict a broad range of outcomes as a function of its parameters