The Arcsine Exponentiated-<i>X</i> Family: Validation and Insurance Application

He, Wenjing; Ahmad, Zubair; Afify, Ahmed Z.; Goual, Hafida

doi:10.1155/2020/8394815

Cited by 24 publications

(23 citation statements)

References 36 publications

(35 reference statements)

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“…Deploying the T-X approach, a good deal of new families of statistical models have been proposed in the literature; see [17][18][19][20] and [21]. Let T � exp (1), then its cdf is given by…”

Section: Proposed Methodsmentioning

confidence: 99%

“…Recently, [ 16 ] proposed the T- X family method that is specified by the cumulative distribution function (cdf) where K [ F ( x ; ξ )] fulfills certain conditions; see [ 16 ]. The probability density function (pdf) corresponding to Eq (1) is Deploying the T- X approach, a good deal of new families of statistical models have been proposed in the literature; see [ 17 – 20 ] and [ 21 ]. Let T ∼ exp(1), then its cdf is given by Corresponding to expression (), the density function is If v ( t ) follows Eq (3) and setting in Eq (1) , the cdf of the type-I heavy-tailed (TI-HT) family follows as where F ( x ; ξ ) is the baseline distribution function which may depend on Form Eq (4) , we can see that G ( x ; θ , ξ ) = F ( x ; ξ ) for θ = 1.…”

Section: Proposed Methodsmentioning

confidence: 99%

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Type-I heavy tailed family with applications in medicine, engineering and insurance

et al. 2020

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In the present study, a new class of heavy tailed distributions using the T-X family approach is introduced. The proposed family is called type-I heavy tailed family. A special model of the proposed class, named Type-I Heavy Tailed Weibull (TI-HTW) model is studied in detail. We adopt the approach of maximum likelihood estimation for estimating its parameters, and assess the maximum likelihood performance based on biases and mean squared errors via a Monte Carlo simulation framework. Actuarial quantities such as value at risk and tail value at risk are derived. A simulation study for these actuarial measures is conducted, proving that the proposed TI-HTW is a heavy-tailed model. Finally, we provide a comparative study to illustrate the proposed method by analyzing three real data sets from different disciplines such as reliability engineering, bio-medical and financial sciences. The analytical results of the new TI-HTW model are compared with the Weibull and some other non-nested distributions. The Baysesian analysis is discussed to measure the model complexity based on the deviance information criterion.

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Section: Proposed Methodsmentioning

confidence: 99%

Section: Proposed Methodsmentioning

confidence: 99%

Type-I heavy tailed family with applications in medicine, engineering and insurance

et al. 2020

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“…In this article, we focus on proposing a new modification of the modified Weibull distribution called the arcsine modified Weibull (ASM-Weibull) distribution. The ASM-Weibull distribution is introduced by adopting the approach of the arcsine-X distributions of [29], which can be obtained as a sub-case of [30]. The cdf and pdf of the arcsine-X distributions are given, respectively, by…”

Section: Plos Onementioning

confidence: 99%

Modeling the survival times of the COVID-19 patients with a new statistical model: A case study from China

et al. 2021

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Over the past few months, the spread of the current COVID-19 epidemic has caused tremendous damage worldwide, and unstable many countries economically. Detailed scientific analysis of this event is currently underway to come. However, it is very important to have the right facts and figures to take all possible actions that are needed to avoid COVID-19. In the practice and application of big data sciences, it is always of interest to provide the best description of the data under consideration. The recent studies have shown the potential of statistical distributions in modeling data in applied sciences, especially in medical science. In this article, we continue to carry this area of research, and introduce a new statistical model called the arcsine modified Weibull distribution. The proposed model is introduced using the modified Weibull distribution with the arcsine-X approach which is based on the trigonometric strategy. The maximum likelihood estimators of the parameters of the new model are obtained and the performance these estimators are assessed by conducting a Monte Carlo simulation study. Finally, the effectiveness and utility of the arcsine modified Weibull distribution are demonstrated by modeling COVID-19 patients data. The data set represents the survival times of fifty-three patients taken from a hospital in China. The practical application shows that the proposed model out-classed the competitive models and can be chosen as a good candidate distribution for modeling COVID-19, and other related data sets.

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“…Hence, bringing flexibility to a model by introducing additional parameter(s) is a desirable feature [ 20 – 24 ]. In a number of recent papers, serious attempts have been made to introduce a variety of new heavy-tailed distributions, see Ahmad et al [ 25 ] and Ahmad et al [ 26 ].…”

Section: Introductionmentioning

confidence: 99%

On Modeling the Earthquake Insurance Data via a New Member of the T-X Family

Ahmad

Mahmoudi

Kharazmi

2020

Computational Intelligence and Neuroscience

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Heavy-tailed distributions play an important role in modeling data in actuarial and financial sciences. In this article, a new method is suggested to define new distributions suitable for modeling data with a heavy right tail. The proposed method may be named as the Z-family of distributions. For illustrative purposes, a special submodel of the proposed family, called the Z-Weibull distribution, is considered in detail to model data with a heavy right tail. The method of maximum likelihood estimation is adopted to estimate the model parameters. A brief Monte Carlo simulation study for evaluating the maximum likelihood estimators is done. Furthermore, some actuarial measures such as value at risk and tail value at risk are calculated. A simulation study based on these actuarial measures is also done. An application of the Z-Weibull model to the earthquake insurance data is presented. Based on the analyses, we observed that the proposed distribution can be used quite effectively in modeling heavy-tailed data in insurance sciences and other related fields. Finally, Bayesian analysis and performance of Gibbs sampling for the earthquake data have also been carried out.

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The Arcsine Exponentiated-X Family: Validation and Insurance Application

Cited by 24 publications

References 36 publications

Type-I heavy tailed family with applications in medicine, engineering and insurance

Type-I heavy tailed family with applications in medicine, engineering and insurance

Modeling the survival times of the COVID-19 patients with a new statistical model: A case study from China

On Modeling the Earthquake Insurance Data via a New Member of the T-X Family

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