Title: Goodness-of-fit tests for the geometric distribution based on conditional moments
Authors: Virtudes Alba-Fernandez - University of Jaen (Spain) [presenting]
Maria Dolores Jimenez-Gamero - Universidad de Sevilla (Spain)
Abstract: The geometric distribution is a discrete law which is popular in life time analysis as a discrete survival distribution. Recently, nice applications in capture-recapture methods have been found. A test is proposed for testing goodness-of-fit to that distribution. The test is based on a characterization of the geometric distribution in terms of the conditional expectation of the second order statistic, given the value of the first order statistic, which is linear if and only if the law is geometric. Then, using the well-known Bierens characterization of conditional moments, a test statistic is proposed. The asymptotic null distribution of the test statistic under general conditions is derived. A parametric bootstrap can be used to consistently approximate the null distribution. The goodness of the bootstrap estimator for finite sample sizes is assessed by simulation. The power of the new test is numerically compared with that of other existing tests, concluding that the proposal shows a competitive behavior.