Generalized hyperbolic secant distribution: Properties, estimation, and applications

Abstract

In this study, we define a generalized hyperbolic secant distribution. Poor fit to heavy tailed data sets is repeatedly obtained by existing three-parameter distributions. Only three parameters are considered in the proposed new distribution and it fits a heavy left- and right-tailed data better than various existing distributions. We study some properties of the new distribution, namely, mode, skewness, kurtosis, hazard function, moments, mean deviation, and Shannon entropy. Seven different frequentist methods for estimating the parameters are briefly described. A simulation study is also conducted to compare the performances of the proposed methods of estimation. The usefulness of the new model is demonstrated by applying it to fit two real-life data.