Goodness-of-fit test for length-biased data with discussion on prevalence, sensitivity and specificity of the length bias

Abstract

Abstract Due to reasons like absence of a proper sampling frame or inaccessibility to population units, data in statistical studies are sometimes contaminated by a phenomenon called length bias (LB). In this article, an asymptotic test statistic is derived to examine the homogeneity of a length biased sample from the Mean Exponential Family (MEF), a new class of distributions introduced by Shanmugam ( J. Statist. Plann. Inference 23 (1989) 227–291). Expressions for the test statistic are obtained for length biased binomial, Poisson, negative binomial, beta, gamma, normal, Pareto, Laplace, and Raleigh distributions as special cases. The results are illustrated. One among several advantages in our approach is the ability to quantify the specificity and sensitivity of LB and their instrinsic relations.