Abstract

ESTIMATIONOF PARAMETERS OF WEIBULL-NORMAL DISTRIBUTION USING MAXIMUM LIKELIHOOD APPROACH

YAHAYA, A. & IEREN, T. G.

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ABSTRACT The Weibull-Normal distribution is a four parameter distribution found to be negatively skewed with better fitness or performance compared to other skewed-Normal distributions. These four parameters include the scale and shape parameters of the Weibull distribution as well as the location and dispersion parameter of the conventional Normal distribution all of which are very important and provides flexibility to this distribution. Datasets that are mounded or bell-shaped are easily found across various fields ofstudy. Although, there is a very high utility and patronage for the Normal distribution; quite often the assumed symmetric nature of some datasets cannot be substantiated. The Weibull-Normal distribution mitigates the inability of the normal distribution to fit these type of skewed datasets and allows for making an informed and qualitative decision. In this article, we made use of the Weibull-G generator proposed by Bourguignon et al. (2014) to define a Weibull-Normal distribution and estimate its four parameters using the method of maximum likelihood. The proposed model was comparedwith other related baseline models based on some standard performance measures using a real life dataset and we found that the Weibull-Normal performs better than the Weibull-Frechetdistribution, Weibull-Exponentail distribution and the conventional Weibull distribution. Keywords: Weibull-Gfamily, Maximum likelihood, Goodness-of-fit test, Probability models.

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