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 cumulative distribution, probability density, survival and hazard functions. The Monte Carlo simulation study is conducted to assess the performances of these estimators. Finally, the adequacy of Gamma-Weibull distribution in data modeling is verified by the two clinical real data sets. Mathematics Subject Classification: 62E99; 62E15

The development of an extended Weibull model with applications to medicine, industry and actuarial sciences

“…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.…”

Exploring the Dynamics of COVID-19 with a Novel Family of Models

“…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:…”

“…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].…”

A new alpha logarithmic-generated class to model precipitation data with theory and inference

“…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.…”