On the Sin-G class of distributions: theory, model and application

Document Type : Research Article


1 PPGBEA, Universidade Federal Rural de Pernambuco, Recife/PE, Brazil

2 Instituto Federal da Pernambuco, Pernambuco/PE, Brazil

3 Universit\'e de Caen, LMNO, Campus II, Science 3, 14032, Caen, France


This paper is devoted to the study of the Sin-G class of distributions and one of its special member. We first explore the mathematical properties of the Sin-G class, giving the cumulative and probability density functions and their expansions, quantile function, moments, moment generating function, reliability parameter, R'enyi entropy and order statistics. Then, we focus our attention on the special member defined with the Inverse Weibull distribution as baseline,  denoted by SinIW. The mathematical and practical aspects of the SinIW distribution are investigated.  In order to illustrate the usefulness of the SinIW model, an application to real life data set is carried out.