Abstract

DISCRIMINATION BETWEEN THE WEIBULL-NORMAL AND THE GENERALIZED WEIBULL-NORMAL DISTRIBUTIONS

IEREN, T. G.&YAHAYA, A.

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ABSTRACT As a result of increased interest in the introduction of new probability distributions over some few decades ago, there arises a major problem in Distribution Theory related to choosing the best distribution thatfits a given dataset. Many a times we are confronted with problems in which two or more distributions tend to fit a particular dataset with very negligible difference in performance. Both Weibull-Normal and Generalized Weibull-Normal distributions have been found (among other well-known distributions) to be negatively skewed and possibly victims of such scenarios. Hence, the problem of making a judicious selection between the two is considered in this paper. Some of the statistical tools used in discriminating and comparing the performance between the two distributions comprise the value of their negative log-likelihood function, Akaike Information Criteria (AIC), Bayesian Information Criteria (BIC), Consistent Akaike Information Criterion (CAIC), and HannanQuin Information Criterion (HQIC). These performance measures were based on the analysis carried out on three different datasets. Keywords: Generalized Weibull-Normal Distribution, Discrimination, log-likelihood.

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