| Practical applied statistics reveals that the analysis of many real data that exhibit both fat-tailless and skewness shows significant departures from normality assumptions. In these circumstances, the adoption of more flexible models that cope with near normal data may be appropriate in place of adopting the robust approach, semi-parametric or nonparametric models, and Box-Cox transformation. An alternative approach is to consider using the Epsilon Skew Exponential Power (ESEP) distribution developed by Elsalloukh and which embeds the normal, fat-tailedness, and skewness distributions as special cases.;We develop models based on using the ESEP family, in particular, the ESEP receiver operating characteristic (ROC) curve with application of the Epsilon Skew Laplace (ESL) ROC curve as a special case of ESEP ROC curve, the ESEP Tobit regression model with application of the ESL Tobit regression. We also introduce a new family of distribution called the Epsilon Skew Double Inverted Weibull (ESDIW) distribution as well as the Exponentiated Inverted Weibull (EIW) distribution. |
