Khalil New Generalized Weibull Distribution Based on Ranked Samples: Estimation, Mathematical Properties, and Application to COVID-19 Data

Emam, Walid; Tashkandy, Yusra

doi:10.3390/sym14050853

Cited by 8 publications

(5 citation statements)

References 8 publications

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“…Suppose the squared error loss function, given by L SE (δ, δ) = (δ − δ) 2 . By using the generated random samples from the M-H technique and for N is the nburn.…”

Section: Ifmentioning

confidence: 99%

“…There are a lot of probability distributions in the science of statistics that have been identified, studied, and entered into many areas of life using real data, but we may face problems in some data because we do not reach realistic results, because the probability distribution is unable to model the data, so we use other methods, namely Mixing or synthesizing distributions. Statistical methods play a crucial role in analysis of medical data [1]- [2], environmental data [3]- [4], engineering data [5]- [6], social data [7], actuarial data [8], test data [9], reliability data [10], sports data [11], educational data [12], measurement system errors [13], risk assessment [14], robust analysis [15].…”

Section: Introductionmentioning

confidence: 99%

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A Bayesian and classical estimation of the new probabilistic Inverted Topp Leone Weibull distribution with application

Alomani

Emam

2023

Preprint

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In this article, we present a new modification of the Weibull model with three parameters for analysing events in the real world, called the new Inverted Topp Leone Weibull distribution. The new model has many statistical advantages. The flexibility of the proposed model has been improved. The proposed model can be used to fit data with different shapes, it can be right skewed, left skewed, decreasing, curved and symmetric. The maximum likelihood approach and Bayesian estimation are used to estimate the distribution parameters. Three different loss functions are used for the Bayesian procedure. The calculations show the biases and estimated risks to obtain the best estimator. The bootstrap confidence intervals, the asymptotic confidence intervals, and the observed variance-covariance matrix are obtained. The Metropolis Hastings MCMC procedure is used for the calculations. We apply the composite distribution to two real data from the medical and engineering fields. The goodnessof-fit results show that it performs well compared to other distributions.

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“…Suppose the squared error loss function, given by L SE (δ, δ) = (δ − δ) 2 . By using the generated random samples from the M-H technique and for N is the nburn.…”

Section: Ifmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A Bayesian and classical estimation of the new probabilistic Inverted Topp Leone Weibull distribution with application

Alomani

Emam

2023

Preprint

Self Cite

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“…For more reading about statistical distributions using different approaches; see, [1]. Statistical methods play a crucial role in analysis of medical data [2,3], environmental data [4,5], engineering data [6,7], social data [8], actuarial data [9], test data [10], reliability data [11], sports data [12], educational data [13], measurement system errors [14], risk assessment [15], robust analysis [16,17].…”

Section: Introductionmentioning

confidence: 99%

A new detection of flexible Weibull model with application

Alomani

Emam

2023

Preprint

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The new family of distributions may provide a better fit to the data than existing families of distributions. This can lead to more accurate modeling and prediction. The new family of distributions may provide insights into the underlying mechanisms that generate the data. This can lead to improved understanding of the phenomenon being studied. The new family of distributions may generalize existing families, allowing for more flexible modeling and analysis. The new family of distributions may have applications in areas where existing families are not suitable or have not been explored. Overall, a new family of distributions can expand the toolkit available to researchers and practitioners, leading to improved modeling, analysis, and understanding in a variety of fields. In this paper, we introduce a new family of distributions, which we call the generalized Weibull exponential family. This family includes several well-known distributions as special cases. One advantage of the generalized Weibull exponential family is its flexibility in modeling a wide range of shapes and scales. It can handle both increasing and decreasing hazard rates, which are important in reliability analysis. Moreover, it can capture heavy-tailed or light-tailed behavior depending on the choice of parameters. In conclusion, we believe that the generalized Weibull exponential family is a useful addition to the existing families of distributions. Its flexibility and tractability make it a promising candidate for modeling data in various applications. Based on the proposed family, we introduce a new model with five parameters, named the generalized Weibull exponential distribution. Some mathematical properties were obtained. Maximum likelihood estimates for the model parameters were derived. A Monte Carlo simulation study was derived to assess the performance of the maximum likelihood estimates. A simulation study based on the parameters of the proposed model was performed. Finally, an application to real data set was performed.

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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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Khalil New Generalized Weibull Distribution Based on Ranked Samples: Estimation, Mathematical Properties, and Application to COVID-19 Data

Cited by 8 publications

References 8 publications

A Bayesian and classical estimation of the new probabilistic Inverted Topp Leone Weibull distribution with application

A Bayesian and classical estimation of the new probabilistic Inverted Topp Leone Weibull distribution with application

A new detection of flexible Weibull model with application

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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