Distribution Theory for Tests Based on Sample Distribution Function

by J. Durbin

Presents a coherent body of theory for the derivation of the sampling distributions of a wide range of test statistics. Emphasis is on the development of practical techniques. A unified treatment of the theory was attempted, e.g., the author sought to relate the derivations for tests on the circle and the two-sample problem to the basic theory for the one-sample problem on the line. The Markovian nature of the sample distribution function is stressed, as it accounts for the elegance of many of the results achieved, as well as the close relation with parts of the theory of stochastic processes.

70 pages, Paperback

First published January 1, 1973

Reviews

[Kevin K. Gillette · Rating 5 out of 5]

When I was an undergraduate in applied mathematics, I often wondered how statistical tests such as the Student-t test, the chi-squared test, and so on, were developed. This excellent monograph by James Durbin answered a lot of those questions for me, and showed me the level of effort required to rigorously prove out the utility of various statistical tests. Definitely a must-read if you've ever had these questions and didn't know where to turn for answers!