A POLYA APPROXIMATION TO THE POISSON-BINOMIAL LAW

作者：Skipper Max^*

来源：Journal of Applied Probability, 2012, 49(3): 745-757.

• Stein's method
• Poisson-binomial approximation
• Bernoulli variable

Using Stein's method, we derive explicit upper bounds on the total variation distance between a Poisson-binomial law (the distribution of a sum of independent but not necessarily identically distributed Bernoulli random variables) and a Polya distribution with the same support, mean, and variance; a nonuniform bound on the pointwise distance between the probability mass functions is also given. A numerical comparison of alternative distributional approximations on a somewhat representative collection of case studies is also exhibited. The evidence proves that no single one is uniformly most accurate, though it suggests that the Polya approximation might be preferred in several parameter domains encountered in practice.

• 出版日期2012-9