The Generalized Alpha Exponent Power Family of Distributions: Properties and Applications

In this article, four new families named as Weibull extended exponentiated-X (WEE-X), Lomax extended exponentiated-X (LEE-X), Logistic extended exponentiated-X (LGCEE-X), and Burr III extended exponentiated-X (BIIIEE-X) with their quantile functions are proposed. The expressions for distribution function and density function of BIIIEE-X family are written in terms of linear combinations of the exponentiated densities based to parent model. New models, i.e., Weibul extended exponentiated Weibull (WEEW), Lomax extended exponentiated Weibull (LEEW), Logistic extended exponentiated Weibull (LGCEEW), and Burr III extended exponentiated-Weibull (BIIIEEW) distributions are derived, were plotted for functions of probability density and hazard rate at different levels of parameters. Some mathematical properties of the BIIIEEW model are disclosed. The maximum likelihood method for the BIIIEEW model are described. Numerical applications of the BIIIEEW model to disease of cancer datasets are provided.

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“…It is also applied to datasets of wages, income, and wealth. For more details on well-known X-classes, review [9,10].…”

Section: Burr III Extended Exponentiated-x (Biiiee-x) Familymentioning

confidence: 99%

Families of Extended Exponentiated Generalized Distributions and Applications of Medical Data Using Burr III Extended Exponentiated Weibull Distribution

et al. 2023

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“…Some of the well-known methods for generating new PDs are included in [5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20]. Other methods to generate flexible PDs are the odd generalized NH-G [21], Marshall-Olkin odd Lindley-G [22], Maxwell-G [23], odd inverse power generalized Weibull-G [24], generalized Rayleigh-G [25], generalized odd linear exponential-G [26], generalized exponential extended exponentiated-G [27] and generalized alpha exponent power-G [28], among others.…”

Section: Introductionmentioning

confidence: 99%

A Novel Odd Beta Prime-Logistic Distribution: Desirable Mathematical Properties and Applications to Engineering and Environmental Data

et al. 2023

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In parametric statistical modeling, it is important to construct new extensions of existing probability distributions (PDs) that can make modeling data more flexible and help stakeholders make better decisions. In the present study, a new family of probability distributions (FPDs) called the odd beta prime generalized (OBP-G) FPDs is proposed to improve the traditional PDs. A new PD called the odd beta prime-logistic (OBP-logistic) distribution has been developed based on the developed OBP-G FPDs. Some desirable mathematical properties of the proposed OBP-logistic distribution, including the moments, moment-generating function, information-generating function, quantile function, stress–strength, order statistics, and entropies, are studied and derived. The proposed OBP-logistic distribution’s parameters are determined by adopting the maximum likelihood estimation (MLE) method. The applicability of the new PD was demonstrated by employing three data sets and these were compared by the known extended logistic distributions, such as the gamma generalized logistic distribution, new modified exponential logistic distribution, gamma-logistic distribution, exponential modified Weibull logistic distribution, exponentiated Weibull logistic distribution, and transmuted Weibull logistic distribution. The findings reveal that the studied distribution provides better results than the competing PDs. The empirical results showed that the new OBP-logistic distribution performs better than the other PDs based on several statistical metrics. We hoped that the newly constructed OBP-logistic distribution would be an alternative to other well-known extended logistic distributions for the statistical modeling of symmetric and skewed data sets.

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“…Some families of continuous probability distributions are available in the literature, including the beta generalized-G family by [67], the beta-G by [65], a novel technique for generating families of continuous probability distributions by [68], the Lindley family of distributions by [69], the Zografos-Balakrishnan-G family of distributions by [70], the Topp-Leone family of distributions by [71], the Kumaraswamy transmuted-G family of distributions by [72], and the exponentiated Gompertz generated family of distributions by [73]. Other distribution families that can be cited are the generalized odd half-Cauchy family of distributions by [74], the odd-Burr generalized family of distributions by [75], the extended odd Fréchet-G family of distributions by [76], the generalized odd Weibull generated family of distributions by [77], the generalized odd gamma-G family of distributions by [78], the modified odd Weibull family of distributions by [79], the odd Dagum family of distributions by [80], the Zubair-G family of distributions by [81], the truncated Burr X-G family of distributions by [82], the alpha power Marshall-Olkin-G distributions by [83], the odd log-logistic Burr-X family of distributions by [84], the Teissier-G family of distributions [85], and the generalized alpha exponent power family of distributions by [86] among others.…”

Section: Introductionmentioning

confidence: 99%

A New Statistical Model Based on the Novel Generalized Odd Beta Prime Family of Continuous Probability Distributions with Applications to Cancer Disease Data Sets

Suleiman¹,

Othman²,

Ishaq³

et al. 2022

Preprint

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Statistical modeling of lifetime data plays an essential role in a wide range of practical fields, such as health and engineering. There have been a lot of studies done to develop statistical models that can better describe health data than traditional models. For the first time, we pioneer a novel family of continuous probability distributions called the generalized odd beta prime generalized (GOBP-G) family of distributions. The cumulative distribution and probability density functions of the new family are presented. A new generalization of the Weibull distribution called "generalized odd beta prime-Weibull" (GOBPW) is proposed using the pioneered GOBP-G family. The mixture representations of the new distribution are defined and derived. Some formal statistical properties of the GOBPW distribution, such as the moments, moment generating function, incomplete moments, information generating function, entropies, stress-strength function, quantile function, and order statistics, are derived. The estimation of the parameters of the proposed distribution is evaluated using the maximum likelihood estimation approach. Different cancer disease data sets, such as the bladder, head and neck, acute bone, and blood cancers, are used to illustrate the applicability and usefulness of the new model and were compared using several statistical accuracy measures with that of well-established extended Weibull distributions, which are the beta modified Weibull distribution, Kumaraswamy modified Weibull distribution, gamma generalized modified Weibull distribution, gamma log-logistic Weibull distribution, and beta log-logistic Weibull distribution. The results show that the proposed model gives better results than the competitive models. This study could guide the relevant stakeholders in choosing a suitable statistical model for the health data instead of relying on traditional models to enhance decision-making.

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The Generalized Alpha Exponent Power Family of Distributions: Properties and Applications

Cited by 7 publications

References 15 publications

Families of Extended Exponentiated Generalized Distributions and Applications of Medical Data Using Burr III Extended Exponentiated Weibull Distribution

Families of Extended Exponentiated Generalized Distributions and Applications of Medical Data Using Burr III Extended Exponentiated Weibull Distribution

A Novel Odd Beta Prime-Logistic Distribution: Desirable Mathematical Properties and Applications to Engineering and Environmental Data

A New Statistical Model Based on the Novel Generalized Odd Beta Prime Family of Continuous Probability Distributions with Applications to Cancer Disease Data Sets

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