Abstract
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.
Highlights
Introduction and motivationStatistical literature contains various G families of distributions which were generated either by compounding common existing G families or by adding one parameters to the existing G families
In this paper we propose and study a new family of distributions using the zero truncated Poisson (ZTP) distribution with a strong physical motivation
Equation (11) reveals that the probability density function (PDF) of quasi-Poisson generalized Weibull-G (QPGW-G) family can be expressed as a linear combination of exp-G PDFs
Summary
Cς(P, Q) = PQ(1 + ςPQ), where the continuous marginal function P ∈ (0,1) and Q ∈ (0,1). The parameter ς ∈ [−1,1] is a dependence parameter. For every Cς(P, 0) = Cς(0, Q) = 0|(P,Q∈(0,1)), which is "grounded minimum" and Cς(P, 1) = P and Cς(1, Q) = Q which is "grounded maximum". The joint PDF (J-CDF) can be derived from cς(P, Q) = 1 + ςP∗Q∗|(P∗=1−2P and Q∗=1−2Q)
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