Extensions for the use of the epsilon -skew -normal distribution for modeling data
Mashtare, Terry L., Jr.
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A common assumption for a number of statistical applications involving continuous data, is to assume the data are normally distributed. In the event the normality assumption is in question Box-Cox transformations to the data or the use of nonparametric and semi-parametric models are often utilized. An alternative approach is to consider utilizing the epsilon-skew-normal (ESN) distribution developed by Mudholkar and Hutson (2000). We create extensions based on the ESN model and apply and extend Tobit models and binormal receiver operating characteristic (ROC) curves. We examine the behavior of the maximum likelihood estimates for model parameters via simulation study and show that they are well behaved. We also introduce a new family of distributions called the log-epsilon-skew-normal (LESN) distribution and derive its properties. We illustrate its utility in the context of accelerated life failure modeling. We will also lay out a plan for our future work.