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Near-exact distributions for the generalized Wilks Lambda statistic based on truncations of the exact distribution
by
Luis Miguel Grilo
Polytechnic Institute of Tomar, Portugal
Coauthors: Carlos Agra Coelho (New University of Lisbon, Portugal)
Once the exact distribution of a Logbeta random variable is expressed under the form of an infinite mixture of Exponential distributions, where the associated series has good convergence properties, we develop an exact distribution for the product of an odd number of independent Beta random variables which involves an infinite mixture of Generalized Integer Gamma (GIG) distributions. By direct application of these results we obtained the exact distribution of the Wilks Lambda statistic used in testing the independence of two groups of variables, both with an odd number of variables, as well as the exact distribution of the generalized Wilks Lambda statistic used in testing the independence of several groups of variables, when at most three of these groups have an odd number of variables. These distributions were obtained under the form of infinite mixtures of GIG distributions and they are more manageable than other known ways to express the exact distribution, with the expressions for the pdf and cdf not involving any unsolved integrals. Then, based on truncations of the exact distributions we were able to obtain near-exact distributions which, by construction, have the two first moments equal to the exact ones and which are relatively easy to implement computationally, allowing for the computation of near-exact quantiles which may indeed be regarded as virtually exact, given the good convergence properties of the series involved, mainly when the difference between the sample size and the overall number of variables involved is rather small.
Date received: October 10, 2005
Copyright © 2005 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # carm-32.