Estimating sample size to approximate some sampling distributions by information measures

Mohammed E.M. Gobar; Eihab B.M. Bashier

Mohammed E.M. Gobar Department of Mathematics, Faculty of Science and Arts, Buljurashi, Al.Baha University, Saudi Arabia
Eihab B.M. Bashier Department of Applied Mathematics, Faculty of Mathematical Sciences, University of Khartoum, Saudi Arabia

Keywords: B-entropy measure, Fisher information measures, Akaike information criterion, approximate distribution, percentage relative error.

Abstract

B-entropy measure, Fisher information measures and Akaikeinformation criterion are considered as three different types of information measures, entropy , parametric and statistical measures respectively. The mainobjective of this paper is to estimate the optimal sample size under which a random variable belonging to Gamma or Poisson distribution can be approximated by a random variable following the normal distribution in the sense of the central limit theorem, based on the concept of the percentage relative error in information due to approximation. The idea is to determining the sample size for which the percentage relative error in information measure is less than a given accuracy level for small.

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