Recent Developments in Distribution Theory: A Brief Survey and Some New Generalized Classes of distributions

Ahmad, Zubair; Hamedani, G. G.; Butt, Nadeem Shafique

doi:10.18187/pjsor.v15i1.2803

Cited by 57 publications

(48 citation statements)

References 11 publications

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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%

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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%

“…where Θ = (α, γ, θ) T . The computer software such as ASS (PROC UNMIXED) can be used to maximize the log-likelihood function directly or via differentiating Eq (17). The partial https://doi.org/10.1371/journal.pone.0237462.g004…”

Section: Maximum Likelihood Estimationmentioning

confidence: 99%

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

et al. 2020

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“…In the practice of big data sciences, particularly in statistical theory, there has be an increased interest in defining new statistical models or new families of statistical models to provide a better description of the problems under consideration; see [6,7]. For more details, we refer to [8]. Often, adding extra parameter(s) gives more flexibility to a class of distribution functions, improves the characteristics, and provides better fits to the real-life data than the other modified models.…”

Section: Proposed Family Of Statistical Modelsmentioning

confidence: 99%

Comparison of COVID-19 Pandemic Dynamics in Asian Countries with Statistical Modeling

Zuo

Khosa

Ahmad

et al. 2020

Computational and Mathematical Methods in Medicine

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In the current scenario, the outbreak of a pandemic disease COVID-19 is of great interest. A broad statistical analysis of this event is still to come, but it is immediately needed to evaluate the disease dynamics in order to arrange the appropriate quarantine activities, to estimate the required number of places in hospitals, the level of individual protection, the rate of isolation of infected persons, and among others. In this article, we provide a convenient method of data comparison that can be helpful for both the governmental and private organizations. Up to date, facts and figures of the total the confirmed cases, daily confirmed cases, total deaths, and daily deaths that have been reported in the Asian countries are provided. Furthermore, a statistical model is suggested to provide a best description of the COVID-19 total death data in the Asian countries.

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“…For the contributed work based on the idea of T-X approach, we refer to Ahmad et al [23]. Using the approach of T-X method, one can introduce new members of survival family [24] via the cdf…”

Section: Introductionmentioning

confidence: 99%

New methods to define heavy-tailed distributions with applications to insurance data

Ahmad

Mahmoudi

Hamedani

et al. 2020

Journal of Taibah University for Science

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Heavy-tailed distributions play an important role in modelling data in actuarial and financial sciences. In this article, nine new methods are suggested to define new distributions suitable for modelling data with an heavy right tail. For illustrative purposes, a special sub-model is considered in detail. Maximum likelihood estimators of the model parameters are obtained and a Monte Carlo simulation study is carried out to assess the behaviour of the estimators. Furthermore, some actuarial measures are calculated. A simulation study based on these actuarial measures is done. The usefulness of the proposed model is proved empirically by means of two real data sets. Finally, Bayesian analysis and performance of Gibbs sampling for the data sets are also carried out.

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Recent Developments in Distribution Theory: A Brief Survey and Some New Generalized Classes of distributions

Cited by 57 publications

References 11 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

Comparison of COVID-19 Pandemic Dynamics in Asian Countries with Statistical Modeling

New methods to define heavy-tailed distributions with applications to insurance data

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