Normal-tangent-logarithm-(G_1,G_2 ): a class of probabilistic distributions depending on two baselines

Abstract

Based on the normal distribution, a new generator of continuous distributions is presented using the monotonic functions  and , such that  and  are the baselines. A study of identifiability of the proposed class is exhibited as well as the series expansions for its cumulative distribution function and probability density function. Additionally, some mathematical properties of the class are discussed, namely, the raw moments, the central moments, the moment generating function, the characteristic function, the derivatives of the log-likelihood function, and a study of the support.  A numerical analysis comprising a simulation study and an application to real data is presented. Comparisons between the proposed model and other well-known models evince its potentialities and modeling benefits.