A New Bivariate Extended Generalized Inverted Kumaraswamy Weibull Distribution

In this paper, a new distribution named as unit-power Weibull distribution (UPWD) defined on interval (0,1) is introduced using an appropriate transformation to the positive random variable of the Weibull distribution. This work offers quantile function, linear representation of the density, ordinary and incomplete moments, moment-generating function, probability-weighted moments, L -moments, TL-moments, Rényi entropy, and MLE estimation. Additionally, several actuarial measures are computed. The real data applications are carried out to underline the practical usefulness of the model. In addition, a bivariate extension for the univariate power Weibull distribution named as bivariate unit-power Weibull distribution (BIUPWD) is also configured. To elucidate the bivariate extension, simulation analysis and application using COVID-19-associated fatality rate data from Italy and Belgium to conform a BIUPW distribution with visual depictions are also presented.

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“…It will be denoted by ðX, YÞ ~BIUPWðΘÞ, where Θ ≕ ð λ, β, θ 1 , θ 2 , θ 3 Þ. The readers are referred to [32][33][34]:…”

Section: Bivariate Extensionmentioning

confidence: 99%

Statistical Analysis of COVID-19 Data: Using A New Univariate and Bivariate Statistical Model

Bantan

Shafiq

Tahir

et al. 2022

Journal of Function Spaces

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“…We give a new G class, the extended generalized inverted Kumaraswamy generated (EGIKw-G) family, considering s ( t ) to be GIKum and using the generator ( W λ ( x , ϑ )/1 − W λ ( x , ϑ )) as D [ W ( x )] in ( 2 ) in order to obtain the distributions which show higher flexibility compared with other commonly used standard distributions; see [ 23 , 24 ]. For W ( x ) some baseline cdf, the expression for the cdf of EGIKw-G class is

…”

Section: Introductionmentioning

confidence: 99%

On the Extended Generalized Inverted Kumaraswamy Distribution

Ramzan

Qamar

Amin

et al. 2022

Computational Intelligence and Neuroscience

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In this work, we provide a new generated class of models, namely, the extended generalized inverted Kumaraswamy generated (EGIKw-G) family of distributions. Several structural properties (survival function sf , hazard rate function hrf , reverse hazard rate function rhrf , quantile function qf and median, s th raw moment, generating function, mean deviation md , etc.) are provided. The estimates for parameters of new G class are derived via maximum likelihood estimation MLE method. The special models of the proposed class are discussed, and particular attention is given to one special model, the extended generalized inverted Kumaraswamy Burr XII (EGIKw-Burr XII) model. Estimators are evaluated via a Monte Carlo simulation MCS . The superiority of EGIKw-Burr XII model is proved using a lifetime data applications.

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“…Some of the recent development in modifications of the Weibull distribution mentioned in the literature include the exponentiated Weibull distribution by [20], Marshall-Olkin extended Weibull distribution by [21], the flexible Weibull extension by [22], the generalized modified Weibull distribution by [23], the Kumaraswamy Weibull distribution by [24], the beta modified Weibull distribution by [25], the beta generalized Weibull distribution [26], the beta inverse Weibull distribution by [27], the Kumaraswamy modified Weibull distribution by [28], the transmuted exponentiated generalized Weibull by [29], the Kumaraswamy transmuted exponentiated additive Weibull by [30], the Topp-Leone generated Weibull by [31]. Other studies that can be cited, including, among others, the Lindley Weibull distribution by [32], half-logistic generalized Weibull distribution by [33], the power generalized Weibull distribution by [34], the modified beta generalized Weibull distribution by [35], the generalized weighted Weibull distribution by [36], the beta exponentiated modified Weibull distribution by [37], the log-normal modified Weibull distribution by [38], the new Kumaraswamy Weibull distribution by [39], the generalized extended exponential Weibull distribution by [40], the Maxwell-Weibull distribution by [41], exponentiated additive Weibull distribution by [42], the flexible additive Weibull distribution by [43], the extended generalized inverted Kumaraswamy Weibull distribution by [44], the exponentiated generalized inverse flexible Weibull distribution by [45], the bivariate extended generalized inverted Kumaraswamy Weibull by [46], and the Khalil new generalized Weibull distribution by [47]. For a detailed review of extensions to the Weibull model, we refer to the works of [48] and [49].…”

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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A New Bivariate Extended Generalized Inverted Kumaraswamy Weibull Distribution

Cited by 6 publications

References 26 publications

Statistical Analysis of COVID-19 Data: Using A New Univariate and Bivariate Statistical Model

Statistical Analysis of COVID-19 Data: Using A New Univariate and Bivariate Statistical Model

On the Extended Generalized Inverted Kumaraswamy Distribution

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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