2021
DOI: 10.1177/09622802211009262
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A family of Gamma-generated distributions: Statistical properties and applications

Abstract: In this paper, we concentrate on the statistical properties of Gamma-X family of distributions. A special case of this family is the Gamma-Weibull distribution. Therefore, the statistical properties of Gamma-Weibull distribution as a sub-model of Gamma-X family are discussed such as moments, variance, skewness, kurtosis and Rényi entropy. Also, the parameters of the Gamma-Weibull distribution are estimated by the method of maximum likelihood. Some sub-models of the Gamma-X are investigated, including the cumul… Show more

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Cited by 11 publications
(6 citation statements)
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“…In “ Modeling of COVID-19 and cancer data ” section, we apply the CBellW model to four medical data sets, and in the following “ Designing a GASP with application to Guinea pigs data ” and “ Actuarial measures with applications to auto-mobile collision claims data ” section, we design a GASP (with application to Guinea pigs data) and compute risk measures by using actuarial data, respectively. We also compare several Weibull-based models such as the complementary Poisson Weibull (CPW) 3 , alpha power Weibull (APW) 13 , transmuted Weibull (TW) 14 , beta Weibull (BW) 15 , Marshall Olkin Weibull (MOW) 16 , Weibull claim (W-claim) 17 , gamma Weibull (GW) 18 , Gull alpha power Weibull (GAPW) 19 , and exponentiated exponential (EE) with the proposed CBellW model.…”
Section: Real-life Applicationsmentioning
confidence: 99%
“…In “ Modeling of COVID-19 and cancer data ” section, we apply the CBellW model to four medical data sets, and in the following “ Designing a GASP with application to Guinea pigs data ” and “ Actuarial measures with applications to auto-mobile collision claims data ” section, we design a GASP (with application to Guinea pigs data) and compute risk measures by using actuarial data, respectively. We also compare several Weibull-based models such as the complementary Poisson Weibull (CPW) 3 , alpha power Weibull (APW) 13 , transmuted Weibull (TW) 14 , beta Weibull (BW) 15 , Marshall Olkin Weibull (MOW) 16 , Weibull claim (W-claim) 17 , gamma Weibull (GW) 18 , Gull alpha power Weibull (GAPW) 19 , and exponentiated exponential (EE) with the proposed CBellW model.…”
Section: Real-life Applicationsmentioning
confidence: 99%
“…The ML estimator ϑ = (α, Θ) T can be derived by maximizing the l ϑ | x;Θ or solving the nonlinear likelihood equations simultaneously by differentiating (12). The partial derivative of l ϑ | x;Θ is provided in the following form for both α and Θ, respectively:…”
Section: Inferencementioning
confidence: 99%
“…As a consequence, generated families (G families) are established by modifying the baseline distribution by one or more additional shape parameters. Some of the well-known families recently developed by notable authors include: the Marshall-Olkin family generated by [9], QRTM by [10], Beta generated by [11], Gamma generated by [12], Kumaraswamy generated by [13], T-X family generated by [14], Weibull generated by [15], Type-I-Half-Logistic generated by [16], Topp-Leone generated by [17], and new power class by [18], to mention a few. Readers who are interested in learning more about the COVID-19 mortality and the analysis are encouraged to refer to the work of Al-Babtain et al [19], Liu et al [20], Nagy et al [21], Hossam et al [22], Riad et al [23], Alsuhabi et al [24], and Meriem et al [25].…”
Section: Introductionmentioning
confidence: 99%
“…Furthermore, the authors of the study draw the readers' attention to several other prominent works in the area of generated classes (G-classes), including those by Marshall and Olkin [ 13 ], Shaw and Buckley [ 14 ], Eugene et al [ 15 ], Pourreza et al [ 16 ], Cordeiro and de Castro [ 17 ], Alzaatreh et al [ 18 ], Bourguignon et al [ 19 ], Cordeiro et al [ 20 ], Al-Shomrani et al [ 21 ], Al Mutairi et al [ 22 ], Al-Babtain et al [ 23 ], Alghamdi and Abd El-Raouf [ 24 ], and numerous others.…”
Section: Introductionmentioning
confidence: 99%