Open AccessA Novel Generator of Continuous Probability Distributions for the Asymmetric Left-skewed Bimodal Real-life Data with Properties and Copulas
Author(s) -
Wahid A. M. Shehata,
Haitham M. Yousof,
Mohamed Aboraya
Publication year - 2021
Publication title -
pakistan journal of statistics and operation research
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.354
H-Index - 15
eISSN - 2220-5810
pISSN - 1816-2711
DOI - 10.18187/pjsor.v17i4.3903
Subject(s) - mathematics , moment generating function , exponential family , bivariate analysis , exponential function , probability density function , generator (circuit theory) , moment (physics) , statistics , statistical physics , mathematical analysis , power (physics) , physics , classical mechanics , quantum mechanics
This paper presents a novel two-parameter G family of distributions. Relevant statistical properties such as the ordinary moments, incomplete moments and moment generating function are derived. Using common copulas, some new bivariate type G families are derived. Special attention is devoted to the standard exponential base line model. The density of the new exponential extension can be “asymmetric and right skewed shape” with no peak, “asymmetric right skewed shape” with one peak, “symmetric shape” and “asymmetric left skewed shape” with one peak. The hazard rate of the new exponential distribution can be “increasing”, “U-shape”, “decreasing” and “J-shape”. The usefulness and flexibility of the new family is illustrated by means of two applications to real data sets. The new family is compared with many common G families in modeling relief times and survival times data sets.