On the Exponential Power Distribution

Abstract

The paper examines the nature of the exponential power distribution (EPD) in terms of its location, µ, scale, β and shape, σ, parameters. It establishes conditions under which the distribution is legitimate and reliable. It derives among others the moment and kurtosis of the distribution as well as the maximum likelihood estimators of the parameters. It then uses data on health to assess the departure of the distribution from normality. Three main softwares are used, namely; EasyFit, MATLAB and Minitab.

In the application, we find that the EPD, for some values of , significantly fits Weight, Height and Body Mass Index out of seven variables covered. We deduce that the EPD would be inappropriate for fitting asymmetrical datasets, since the variables which are not significant are found to be highly skewed.

Keywords: Exponential power distribution, Kurtosis, Legitimacy, Statistical Distributions