A normal approximation theorem in comparing two binomial distributions

Haiyan Cai

Statistics & Probability Letters, 2000, vol. 48, issue 1, 83-89

Abstract: Let p0 and be the parameters of two independent binomial distributions. Suppose p0 is known and has a prior distribution with a density function which is positive and continuous at p0. We introduce a normal approximation theorem for approximating the posterior distribution of the scaled difference , given that the difference of the corresponding binomial random variables increases slowly ([less-than-or-equals, slant]n[gamma], ). The theorem is proved based on a local limit theorem which links the probability of the difference of two independent and nearly identical binomial random variables to the density function of a normal distribution.

Keywords: Normal; approximation; Binomial; distribution; Local; limit; theorem; Bayesian; statistics (search for similar items in EconPapers)
Date: 2000
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