On Odd Perks-G Class of Distributions: Properties, Regression Model, Discretization, Bayesian and Non-Bayesian Estimation, and Applications

• Published in: Symmetry (Basel) Vol. 14; no. 5; p. 883
• Main Authors: Elbatal, Ibrahim, Alotaibi, Naif, Almetwally, Ehab M., Alyami, Salem A., Elgarhy, Mohammed
• Format: Journal Article
• Language: English
• Published: Basel MDPI AG 01-05-2022
• Subjects: Actuarial science; Bayesian analysis; Bayesian estimation; COVID-19 data; Discretization; discretization method; entropy; Estimates; Parameters; Perks class; Random variables; regression model; Regression models; Statistical analysis; Weibull distribution
• ISSN: 2073-8994; 2073-8994
• DOI: 10.3390/sym14050883

In this paper, we present a new univariate flexible generator of distributions, namely, the odd Perks-G class. Some special models in this class are introduced. The quantile function (QFUN), ordinary and incomplete moments (MOMs), generating function (GFUN), moments of residual and reversed residual lifetimes (RLT), and four different types of entropy are all structural aspects of the proposed family that hold for any baseline model. Maximum likelihood (ML) and maximum product spacing (MPS) estimates of the model parameters are given. Bayesian estimates of the model parameters are obtained. We also present a novel log-location-scale regression model based on the odd Perks–Weibull distribution. Due to the significance of the odd Perks-G family and the survival discretization method, both are used to introduce the discrete odd Perks-G family, a novel discrete distribution class. Real-world data sets are used to emphasize the importance and applicability of the proposed models.