A normal approximation theorem in comparing two binomial distributions

✍ Scribed by Haiyan Cai

• Publisher: Elsevier Science
• Year: 2000
• Tongue: English
• Weight: 98 KB
• Volume: 48
• Category: Article
• ISSN: 0167-7152
• DOI: 10.1016/s0167-7152(99)00192-3

✦ Synopsis

Let p0 and p be the parameters of two independent binomial distributions. Suppose p0 is known and p 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 di erence √ n( p -p0), given that the di erence of the corresponding binomial random variables increases slowly (6n , 6 1 2 ). The theorem is proved based on a local limit theorem which links the probability of the di erence of two independent and nearly identical binomial random variables to the density function of a normal distribution.