Extended arcsine distribution to proportional data: Properties and applications

Abstract

We propose a new two-parameter continuous model called the extended arcsine distribution restricted to the unit interval. It is a very competitive model to the beta and Kumaraswamy distributions for modeling percentages, rates, fractions and proportions. We provide a mathematical treatment of the new distribution including explicit expressions for the ordinary and incomplete moments, mean deviations, Bonferroni and Lorenz curves, generating and quantile functions, Shannon entropy and order statistics. Maximum likelihood is used to estimate the model parameters and the expected information matrix is determined. We demonstrate by means of two applications to proportional data that it can give consistently a better fit than other important statistical models.

The Exponentiated Generalized Extended Pareto Distribution

“…Henceforth, we denote by X a random variable having pdf (6). For a = b = 1, equation 6reduces to the EP density.…”

“…Often it may be difficult or even impossible to obtain explicit analytical solutions for certain mathematical quantities using directly equation (6). For this reason, it is very common to adopt expansions that allow to obtain simpler expressions for these quantities.…”

“…The above properties and many others have been discussed and explored in recent works for the EG class. Here, we refer to the papers and baseline distributions: [4] for the Birnbaum-Saunders distribution, [8] for the generalized gamma model, [27] for the Dagum distribution, [10] for the Gumbel model, [6] for the arcsine distribution, [9] for an extended exponential model, [23] for the exponential distribution, [26] for the half-normal model.…”

Transforming data with the arcsine distribution for random walks

“…Researchers have been motivated to develop novel models by introducing additional shape parameters into fundamental distributions. For instance, in 2013 [13], the authors introduced the transmuted Log-Logistic distribution, while in 2016 [14], others proposed the extended arcsine distribution, a continuous model characterized by two parameters, achieved through the method of exponentiated generalized. The distribution of the quadratic formula (L), accompanied by a comprehensive study of distribution characteristics was presented in [15].…”