Confidence Intervals for a Ratio of Binomial Proportions Based on Unbiased Estimators

Abstract

A general statement of the interval estimation problem of two proportions ratio according to data from two independent samples is considered. Each sample may be obtained in the framework of direct or inverse binomial sampling. Five asymptotic confidence intervals are constructed in accordance with different types of sampling schemes. Main probability characteristics of intervals are investigated by the Monte-Carlo method: coverage probability, median, expectation and standard deviation of intervals length. The results of the simulations are presented in tables and some recommendations for an application of each of the intervals obtained is presented. Sufficiently complete review of the literature for the problem is also presented.