Author(s)

Thu Pham-Gia¹, Nguyen Van Thin², Phan Phuc Doan²

¹Department of Mathematics and Statistics, Université de Moncton, New Brunswick, Canada.
²Faculty of Mathematics and Computer Science, Hochiminh University of Science, Ho Chi Minh, Vietnam.

Let π=π₁-π₂ be the difference of two independent proportions related to two populations. We study the test H₀:π≥0 against different alternatives, in the Bayesian context. The various Bayesian approaches use standard beta distributions, and are simple to derive and compute. But the more general test H₀:π≥η, with η＞0, requires more advanced mathematical tools to carry out the computations. These tools, which include the density of the difference of two general beta variables, are presented in the article, with numerical examples for illustrations to facilitate comprehension of results.

Proportion, Convolution, Normal, Beta, Bayesian, Critical Value, Appell’s Function

Pham-Gia, T. , Thin, N. and Doan, P. (2017) Inferences on the Difference of Two Proportions: A Bayesian Approach. Open Journal of Statistics, 7, 1-15. doi: 10.4236/ojs.2017.71001.