On the skewed sinh-normal distribution

Abstract

Leiva et al. [10] introduce the skewed sinh-normal distribution, which is a skewed version of the sinh-normal distribution, discussed some of its properties and characterized an extension of the Birnbaum-Saunders distribution associated with this distribution. In this paper, we will introduce further properties of the skewed sinh-normal distribution, and introduce a new approximate form of its probability density function and cumulative distribution function (cdf), along with numerical comparison between the exact and approximate values of its cdf. Moreover, a random number generator for the distribution will be suggested and a goodness of fit test will be carried out to examine the effectiveness of the proposed random number generator. Finally, maximum likelihood estimation for the unknown parameter of the skewed sinh-normal distribution will be investigated, and numerical illustration for the new results will be discussed.