A Family of Skew-Normal Distributions for Modeling Proportions and Rates with Zeros/Ones Excess

Abstract

In this paper, we consider skew-normal distributions for constructing new a distribution which allows us to model proportions and rates with zero/one inflation as an alternative to the inflated beta distributions. The new distribution is a mixture between a Bernoulli distribution for explaining the zero/one excess and a censored skew-normal distribution for the continuous variable. The maximum likelihood method is used for parameter estimation. Observed and expected Fisher information matrices are derived to conduct likelihood-based inference in this new type skew-normal distribution. Given the flexibility of the new distributions, we are able to show, in real data scenarios, the good performance of our proposal.

The unit generalized half-normal quantile regression model: formulation, estimation, diagnostics, and numerical applications

“… 2019 ; Martinez-Florez et al. 2020 ). Moreover, censored observations and frailty models could be investigated in the present context (Leao et al.…”

“…( 2018 ); Kizilaslan and Nadar ( 2018 ); Kohansal ( 2019 ); Martinez-Florez et al. ( 2020 ); Mazucheli et al. ( 2020b ); and Korkmaz et al.…”

A New Quantile Regression for Modeling Bounded Data under a Unit Birnbaum–Saunders Distribution with Applications in Medicine and Politics

“…Other topics of future research are related to studying how multivariate, spatial, temporal structures could be added into the quantile regression framework [58][59][60][61]. In addition, Tobit and Cobb-Douglas type frameworks may be analyzed in the thematic of this investigation [62,63]. Moreover, censored observation might be studied in the present context [64].…”

A Study on Computational Algorithms in the Estimation of Parameters for a Class of Beta Regression Models

“…Modeling of limited-range continuous data is considered in diverse areas when describing indexes, proportions, rates, and ratios, such as in economics and finance [1][2][3][4][5], biology [6], business [7], medicine [8], mining [9], education and psychology [10][11][12][13], and politics [14]. It is worth noting that a package developed in the R software (http: //www.r-project.org accessed on 6 January 2022) allows the beta regression to be applied [15].…”