Abstract

THEORETICAL ANALYSIS OF THE GENERALIZED WEIBULL-NORMAL DISTRIBUTION

Samson Kuje*; Jamila Abdullahi**; Terna Godfrey Ieren**

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Abstract: This paper presents an extension of the normal distribution called the Generalized Weibull-Normal distribution which provides greater ?exibility in modeling scenarios involving skewed datasets than the conventional normal distribution. The probability density function (pdf) and the cumulative distribution function (cdf) of the new distribution were defined using the idea of Weibull-G family proposed by Cordeiro et al. (2015). Analytical expressions for some mathematical quantities comprising moments, moment generating function, characteristics function, reliability functions and order statistics were presented. The estimation of the proposed distributions’ parameters was undertaken using the method of maximum likelihood. Finally, graphical illustrations and analysis are presented with recommendations for applications. Keywords: Weibull-G family, moments, moment generating function, order statistics, Maximum likelihood Estimation.

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