Stochastic orderings, folded beta distributions and fairness in coin flips
نویسندگان
چکیده
This paper studies stochastic orderings for folded beta distributions. A necessary and sufficient condition for one folded beta random variable to be larger than another in likelihood ratio order is obtained. The work is motivated by the recent results of Porzio and Ragozini on stochastic orderings for folded binomial distributions. Beta distributions are commonly used to model proportions or probabilities, particularly as conjugate distributions for binomial random variables. Stochastic orderings may arise, for instance, in considerations of fairness in coin flips. © 2011 Elsevier B.V. All rights reserved.
منابع مشابه
Hessian Stochastic Ordering in the Family of multivariate Generalized Hyperbolic Distributions and its Applications
In this paper, random vectors following the multivariate generalized hyperbolic (GH) distribution are compared using the hessian stochastic order. This family includes the classes of symmetric and asymmetric distributions by which different behaviors of kurtosis in skewed and heavy tail data can be captured. By considering some closed convex cones and their duals, we derive some necessary and s...
متن کاملSome Results on Equilibrium Distributions
The equilibrium distributions have many applications in reliability theory, stochastic orderings and random processes. The purpose of this paper is to introduce the equilibrium distributions and presents some results related to this issue. Some results are based on order statistics. In this paper, the generalized Pareto distributions are also analyzed and some basic relationships between t...
متن کاملA stochastic programming perspective on nonparametric Bayes
We use Church, a Turing-universal language for stochastic generative processes and the probability distributions they induce, to study and extend several objects in nonparametric Bayesian statistics. We connect exchangeability and de Finetti measures with notions of purity and closures from functional programming. We exploit delayed evaluation to provide finite, machine-executable representatio...
متن کاملSome New Results on Stochastic Orderings between Generalized Order Statistics
In this paper we specify the conditions on the parameters of pairs of gOS’s under which the corresponding generalized order statistics are ordered according to usual stochastic ordering, hazard rate ordering, likelihood ratio ordering and dispersive ordering. We consider this problem in one-sample as well as two-sample problems. We show that some of the results obtained by Franco et al. ...
متن کاملPreservation of Stochastic Orderings of Interdependent Series and Parallel Systems by Componentwise Switching to Exponentiated Models
This paper discusses the preservation of some stochastic orders between two interdependent series and parallel systems when the survival and distribution functions of all components switch to the exponentiated model. For the series systems, the likelihood ratio, hazard rate, usual, aging faster, aging intensity, convex transform, star, superadditive and dispersive orderings, and for the paralle...
متن کامل