An extended Gompertz-Makeham distribution with application to lifetime data

El-Bar, Ahmed M. T. Abd

doi:10.1080/03610918.2017.1348517

Cited by 12 publications

(8 citation statements)

References 24 publications

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“…e first data set is: "1.7, 2.5, 27.4, 1.0, 27.1, 2.2, 22.9, 1.7, 0.1, 1.1, 14.4, 1.1, 0.4, 20.6, 5.3, 0.7, 1.9, 13.0, 12.0, 9.3, 1.4, 18.7, 8.5, 25.5, 11.6, 21.5, 27.6, 36.4, 2.7, 14.1, 22.1, 1.1, 2.5, 14.4, 1.7, 37.6, 0.6, 2.2, 39.0, 0.3, 15.0, 11.0, 7.3, 0.6, 9.0, 1.7, 7.0, 20.1, 0.4, 2.8, 14.1, 9.9, 10.4, 10.7, 30.0, 3.6, 5.6, 30.8, 13.3, 4.2, 25.5, 3.4, 11.9, 64.0, 1.5, 20.2, 16.8, 5.3, 9.7, 27.5, 2.5 and 7.0." e fit of the proposed model are compared with the transmuted Gompertz-Makeham (TGM) (Abd El-Bar [29]), beta generalized Gompertz (BGG) (Benkhelifa [30]), kumaraswamy gompertz makeham (KGM) (Chukwu and Ogunde [5]), Gompertz Lomax (GL) (Oguntunde et al [31]), exponentiated generalized Weibull-Gompertz (EGWG) (El-Bassiouny et al [32]), generalized Gompertz (GG) (El-Gohary et al [33]) and Gompertz models.…”

Section: First Real Data Of Flood Peaksmentioning

confidence: 99%

[Retracted] Classical and Bayesian Inference of Marshall‐Olkin Extended Gompertz Makeham Model with Modeling of Physics Data

Mohamed

Al-Babtain

Elbatal

et al. 2022

Journal of Mathematics

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The purpose of this study is to present the Marshall- Olkin extended Gompertz Makeham MOEGM lifetime distribution, which has four parameters. As a result, we will describe some of the structural elements that are introduced for this model. The maximum likelihood approach is used to estimate the model parameters, and it is well known that likelihood estimators for unknown parameters are not always available. As a result, we examine the prior distributions, which allow for prior dependence among the components of the parameter vector, as well as the Bayesian estimators derived with respect to the squared error loss function. A Monte Carlo simulation research is carried out to examine the performance of the likelihood estimators and the Bayesian technique. Finally, we demonstrate the significance of the new model. And to conclude, we illustrate the importance of the new model by exploring some of the empirical applications of physics to show it’s flexibility and potentiality of a new model.

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Section: First Real Data Of Flood Peaksmentioning

confidence: 99%

[Retracted] Classical and Bayesian Inference of Marshall‐Olkin Extended Gompertz Makeham Model with Modeling of Physics Data

Mohamed

Al-Babtain

Elbatal

et al. 2022

Journal of Mathematics

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“…The basic motivation of these transmuted extensions of Gompertz-Makeham distribution is to improve the flexibility of the mortality model and provide better fit for real data in the empirical analysis. An example involves the transmuted Gompertz-Makeham (TGM) distribution proposed by El-Bar et al (2018). He considers this extension in order to handle several particular forms of the hazard rate function, such as the bathtub-shaped function and constant hazard function.…”

Section: Gompertz and Makeham Laws Of Mortalitymentioning

confidence: 99%

Actuarial (Mathematical) Modeling of Mortality and Survival Curves

Brockett¹,

Zhang²

2019

Handbook of the Mathematics of the Arts and Sciences

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This chapter reviews the history, development, and application of mathematical mortality models. It consists of four sections. The first section focuses on parametric mortality models for single individuals. It starts with the innovation involved in creating a mathematical model of mortality, the importance, and the application of mortality tables, followed by the mathematical evolution of mortality models. It ends with the most recent model formulation -the stochastic mortality model. Next, the second section introduces parametric joint mortality models for coupled lives. It covers both the deterministic and stochastic model settings. Joint mortality models for coupled lives have great potential in the insurance industry for pricing joint and last survivor life insurance and annuity products (including pension products). As shown in previous studies, health condition and the expected life length of an individual can be significantly impacted by his or her significant partner, so consideration of bivariate mortality models can have significant practical importance. The third section summarizes nonparametric mortality models, for both individual and coupled lives. Compared with parametric models, the nonparametric ones are free of distributional assumptions and accordingly have a wider and more robust applications when understanding and parametrically modeling the true mortality distribution is not the focus of the study (e.g., when the focus is on studying the effects of covariates on mortality progression rather than mortality itself). Finally, in the fourth section, longevity risk and longevity risk models are introduced. These models are different from the mathematical models in previous sections in that these longevity risk models describe the changes of life expectancy between generations of individuals taking into consideration the cohort effects of people born in different years. These models have a great potential in solving longevity risk problems such as those occur in individual financial planning, institutional portfolio management, social security and medical insurance at a country level.

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“…Many authors applied the aforementioned methods and other methods that are not mentioned here to classical distributions such as the Rayleigh distribution (Merovci [9]), the Gompertz distribution (Abdul-Moniem and Seham [1]), the Gompertz-Makeham distribution (El-Bar [5]), the Skew-Reflected-Gompertz distribution (Contreras-Reyes et al [3]), and the Weibull distribution (khan et al [8]), etc. A new distribution can be generated from a distribution with a cdf G(x) by using this equation…”

Section: Introductionmentioning

confidence: 99%

A New Method of Generating Life-Time Distributions

Riffi

2022

Preprint

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Abstract. Statisticians are interested in improving the ability of classical distributions to appropriately fit real-world data and accurately describe its characteristics. Typically, this can be achieved by extending known distributions by incorporating extra parameters or compounding distributions. In this paper, a flexible general method to obtain new families of distributions is proposed. A number of known methods turn out to be special cases of the proposed method in this paper. Some examples are given to demonstrate the power of the proposed method such as the exponential and the Weibull distribution.

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An extended Gompertz-Makeham distribution with application to lifetime data

Cited by 12 publications

References 24 publications

[Retracted] Classical and Bayesian Inference of Marshall‐Olkin Extended Gompertz Makeham Model with Modeling of Physics Data

[Retracted] Classical and Bayesian Inference of Marshall‐Olkin Extended Gompertz Makeham Model with Modeling of Physics Data

Actuarial (Mathematical) Modeling of Mortality and Survival Curves

A New Method of Generating Life-Time Distributions

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