Stein's Method and Stochastic Orderings
Copyright policy )Stein's Method and Stochastic Orderings
A stochastic ordering approach is applied with Stein's method for approximation by the equilibrium distribution of a birth-death process. The usual stochastic order and the more generals-convex orders are discussed. Attention is focused on Poisson and translated Poisson approximations of a sum of dependent Bernoulli random variables, for example,k-runs in independent and identically distributed Bernoulli trials. Other applications include approximation by polynomial birth-death distributions.
- University of Zurich Switzerland
- Université Libre de Bruxelles Belgium
- University of Bristol United Kingdom
- University of Nottingham United Kingdom
polynomial birth-death approximation, Approximations to statistical distributions (nonasymptotic), (in)dependent indicators, Sciences actuarielles, 60F05, Branching processes (Galton-Watson, birth-and-death, etc.), FOS: Mathematics, (translated) Poisson approximation, Inequalities; stochastic orderings, birth-death processes, total variation distance, 60J80, Probability (math.PR), Central limit and other weak theorems, (approximate) local dependence, stochastic ordering, k-runs, birth-death process, 62E17, Stein's method, total negative and positive dependence, 62E17 (Primary) 60F05, 60J80 (Secondary), Mathematics - Probability
polynomial birth-death approximation, Approximations to statistical distributions (nonasymptotic), (in)dependent indicators, Sciences actuarielles, 60F05, Branching processes (Galton-Watson, birth-and-death, etc.), FOS: Mathematics, (translated) Poisson approximation, Inequalities; stochastic orderings, birth-death processes, total variation distance, 60J80, Probability (math.PR), Central limit and other weak theorems, (approximate) local dependence, stochastic ordering, k-runs, birth-death process, 62E17, Stein's method, total negative and positive dependence, 62E17 (Primary) 60F05, 60J80 (Secondary), Mathematics - Probability
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