A generalized transmuted uniform distribution

Riffi, Mohamed I.; Ansari, Saiful Islam; Hamdan, Mohammed S.

doi:10.1007/s40863-021-00217-4

Cited by 5 publications

(5 citation statements)

References 9 publications

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“…These data were reported in by Riffi et.al [17]. The data was collected from a group of 46 patients, per years, upon the recurrence of leukemia who received autologous marrow.…”

Section: Second Data Setmentioning

confidence: 97%

A new Lifetime Distribution Based on the Transmuted First Two Lower Records

Erbayram

YILDIRIM

Akdoğan

2022

Cumhuriyet Science Journal

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This article introduces a new lifetime distribution by merging the first two lower records based on exponential distribution and discusses the different features of the distribution. Statistical inferences about the distribution parameters are discussed with three estimation methods, namely maximum likelihood, least squares, and weighted least squares. Monte Carlo simulation study is performed to evaluate of these estimators based on mean square errors estimation, mean absolute deviation, and mean relative errors of estimation for a sample of different sizes. A distribution simulation analysis based on real data is provided to demonstrate the adaptability of the proposed model.

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“…These data were reported in by Riffi et.al [17]. The data was collected from a group of 46 patients, per years, upon the recurrence of leukemia who received autologous marrow.…”

Section: Second Data Setmentioning

confidence: 97%

A new Lifetime Distribution Based on the Transmuted First Two Lower Records

Erbayram

YILDIRIM

Akdoğan

2022

Cumhuriyet Science Journal

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“…To introduce a general framework within which different extensions of the Gompertz-Makeham distribution can be derived, Riffi (2018) further proposed a generalized transmuted Gompertz-Makeham (GTGM) distribution by adding two additional parameters in the model. Specifically, the cumulative distribution function of GTGM is…”

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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“…Transmutation was proposed by Shaw and Buckley [12] to extend some non-Gaussian distributions by incorporating new parameters. Transmuted distributions provide tools to adjust the skewness and kurtosis of the distribution so that statisticians may efficiently fit real world data (Riffi et al [10]).…”

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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A generalized transmuted uniform distribution

Cited by 5 publications

References 9 publications

A new Lifetime Distribution Based on the Transmuted First Two Lower Records

A new Lifetime Distribution Based on the Transmuted First Two Lower Records

Actuarial (Mathematical) Modeling of Mortality and Survival Curves

A New Method of Generating Life-Time Distributions

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