General properties for the beta extended half-normal model

Abstract

We formulate and study a four-parameter lifetime model called the beta extended half-normal distribution. This model includes as sub-models the exponential, extended half-normal and half-normal distributions. We derive expansions for the new density function which do not depend on complicated functions. We obtain explicit expressions for the moments and incomplete moments, generating function, mean deviations, Bonferroni and Lorenz curves and Rényi entropy. In addition, the model parameters are estimated by maximum likelihood. We provide the observed information matrix. The new model is modified to cope with possible long-term survivors in the data. The usefulness of the new distribution is shown by means of two real data sets.