Epsilon Half-Normal Model: Properties and Inference Luis M. Castro a , H´ ector W. G´omez b,* , Maria Valenzuela a a Departamento de Estad´ ıstica, Facultad de Ciencias F´ ısicas y Matem´aticas, Universidad de Concepci´ on, Concepci´on, Chile. b Departamento de Matem´aticas, Facultad de Ciencias B´asicas, Universidad de Antofagasta, Antofagasta, Chile. Abstract The half-normal distribution is one of the widely used probability distri- bution for non-negative data modeling, specifically, to describe the lifetime process under fatigue. In this paper, we introduce a new type of non-negative distribution that extends the half-normal distribution. We refer to this new distribution as the epsilon half-normal distribution. We provide mathemati- cal properties of this new distribution. In particular, we derive the stochastic representation, explicit formulas for the n-th moment, the asymmetry and kurtosis coefficients and the moment generating function. We also discuss some inferential aspects related to the maximum likelihood estimation. We illustrate the flexibility of this type of distribution with an application to a real dataset of stress-rupture. Keywords: EM algorithm, epsilon skew-symmetric distribution, half-normal distribution, nonnegative distributions, stochastic representation. * Corresponding author. Tel.: +56 55 637 278; fax +56 55 637 803 Email address: hgomez@uantof.cl (H´ ector W. G´ omez) Preprint submitted to Computational Statistics and Data Analysis April 17, 2012