2020
DOI: 10.1002/cmm4.1135
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A weighted general family of distributions: Theory and practice

Abstract: In this article, we introduce a new general family of distributions. The submodels of the general family accommodate various shapes of pdf and hazard rate, involving decreasing, increasing, bathtub and J-shapes. Hence, it can provide analysis for many practical datasets. Mathematical expressions for the family are obtained, including moments, moment generating and quantile functions, stochastic ordering, and entropy. Some submodels of the family are inserted based on the baseline distributions: Exponential, Go… Show more

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Cited by 9 publications
(7 citation statements)
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“…Let đ‘„ = ∑ 𝑛 𝑖=1 (đ‘„ 𝑖 − đ‘„) 2 . By equating these values with the theoretical moments, we have the estimates of đ›Œ and 𝛿 as:…”
Section: Methods Of Momentsmentioning
confidence: 99%
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“…Let đ‘„ = ∑ 𝑛 𝑖=1 (đ‘„ 𝑖 − đ‘„) 2 . By equating these values with the theoretical moments, we have the estimates of đ›Œ and 𝛿 as:…”
Section: Methods Of Momentsmentioning
confidence: 99%
“…The reason being that the later has closed form expressions for the survival and hazard functions, whereas the former needs numerical integration. For details on the Weibull distribution, see Murthy et al 1 Bakouch et al 2 developed a weighted general family of distributions. We consider a density function of the following type:…”
Section: Introductionmentioning
confidence: 99%
“…In this section, we define the CDF and the PDF of ExRK distribution, respectively, by using the WD-G family of [10] and CDF in equation (1) as follows: 2 Complexity…”
Section: Formulation Of Exrk Distributionmentioning
confidence: 99%
“…Our motivation for developing a new flexible version of the RKD, which we refer to as the extended reduced Kies distribution (ExRKD), is to provide greater flexibility in fitting real-world data sets. Furthermore, the article's main objectives are as follows: e first objective is dedicated to the investigation of a novel version of the RKD based on the weighted-G (WD-G) family [10], which is referred to as the ExRKD.…”
Section: Introductionmentioning
confidence: 99%
“…In this section we define the formulation of the proposed model. Using the cumulative distribution function (CDF) of the WD-G [20], so we can define the CDF of the two-parameter WBHD as follows…”
Section: Formulation Of the Wbhdmentioning
confidence: 99%