Parameter-free testing of the shape of a probability distribution

Broom, M, Nouvellet, P, Bacon, J P and Waxman, D (2007) Parameter-free testing of the shape of a probability distribution. BioSystems, 90 (2). pp. 509-515. ISSN 0303-2647

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The Kolmogorov-Smirnov test determines the consistency of empirical data with a particular probability distribution. Often, parameters in the distribution are unknown, and have to be estimated from the data. In this case, the Kolmogorov-Smirnov test depends on the form of the particular probability distribution under consideration, even when the estimated parameter-values are used within the distribution. In the present work, we address a less specific problem: to determine the consistency of data with a given functional form of a probability distribution (for example the normal distribution), without enquiring into values of unknown parameters in the distribution. For a wide class of distributions, we present a direct method for determining whether empirical data are consistent with a given functional form of the probability distribution. This utilizes a transformation of the data. If the data are from the class of distributions considered here, the transformation leads to an empirical distribution with no unknown parameters, and hence is susceptible to a standard Kolmogorov-Smirnov test. We give some general analytical results for some of the distributions from the class of distributions considered here. The significance level and power of the tests introduced in this work are estimated from simulations. Some biological applications of the method are given. © 2007 Elsevier Ireland Ltd. All rights reserved.

Item Type: Article
Additional Information: Pierre Nouvellet, my joint graduate student with David Waxman, made the observations that underlie this paper.
Schools and Departments: School of Life Sciences > Evolution, Behaviour and Environment
Depositing User: Mark Broom
Date Deposited: 06 Feb 2012 21:29
Last Modified: 16 Aug 2018 09:22
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