A New Extended Geometric Distribution: Properties, Regression Model, and Actuarial Applications

Almazah, Mohammed M. A.; Erbayram, Tenzile; Akdoğan, Yunus; Sobhi, Mashail M. Al; Afify, Ahmed Z.

doi:10.3390/math9121336

Cited by 7 publications

(3 citation statements)

References 18 publications

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“…In this section, the maximum likelihood, least square, weighted least square, Anderson-Darling, Cramer-von Mises, and maximum product spacing methods are discussed to estimate the MoL distribution parameters. It is noticed that these estimates are also used in [2], [13], [14], [29], [30] among others. Let X 1 , X 2 , .…”

Section: Point Estimationmentioning

confidence: 99%

Modified-Lindley distribution and its applications to the real data

Kuş¹,

Korkmaz²,

Kınacı³

et al. 2022

Communications Faculty of Science University of Ankara Series A1Mathematics and Statistics

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In this paper, a new three-parameter lifetime distribution is proposed by mixing modified Weibull and generalized gamma distributions. The point estimation on the distribution parameters are discussed through several estimators. The interval estimation is also studied with two methods based on asymptotic normality and likelihood ratio. A Monte Carlo simulation study is performed to evaluate the biases and mean square errors behaviors of point estimates for a different sample of size. A simulation study is also conducted to investigate the coverage probabilities of confidence intervals. The distribution modeling analyses are provided based on several real data sets to demonstrate the fitting ability of the introduced distribution.

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Section: Point Estimationmentioning

confidence: 99%

Modified-Lindley distribution and its applications to the real data

Kuş¹,

Korkmaz²,

Kınacı³

et al. 2022

Communications Faculty of Science University of Ankara Series A1Mathematics and Statistics

Self Cite

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“…Here, a discretization approach was applied to create a flexible discrete probabilistic model with one parameter. Because of the flexibility of the discretization approach, it has been used by many authors in the statistical literature to produce adaptive discrete models; for instance, discrete Rayleigh distribution by Roy [2], discrete Burr and discrete Pareto distributions by Krishna and Pundir [3], the generalization of geometric distribution by Gomez-Déniz [4], discrete inverse Weibull distribution by Jazi et al [5], discrete Burr Type III distribution by Al-Huniti and Al-Dayian [6], the discrete generalized exponential distribution of the second type by Nekoukhou et al [7], discrete inverse Rayleigh distribution by Hussain and Ahmad [8], two-parameter discrete Lindley distribution by Hussain et al [9], discrete Lindley distribution by Abebe and Shanker [10], new discrete Lindley distribution by Al-Babtain et al [11], new three-parameter discrete Lindley distribution by Eliwa et al [12], and new extended geometric distribution by Almazah et al [13].…”

Section: Introductionmentioning

confidence: 99%

An Extension of the Poisson Distribution: Features and Application for Medical Data Modeling

2023

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This paper introduces and studies a new discrete distribution with one parameter that expands the Poisson model, discrete weighted Poisson Lerch transcendental (DWPLT) distribution. Its mathematical and statistical structure showed that some of the basic characteristics and features of the DWPLT model include probability mass function, the hazard rate function for single and double components, moments with auxiliary statistical measures (expectation, variance, index of dispersion, skewness, kurtosis, negative moments), conditional expectation, Lorenz function, and order statistics, which were derived as closed forms. DWPLT distribution can be used as a flexible statistical approach to analyze and discuss real asymmetric leptokurtic data. Moreover, it could be applied to a hyperdispersive data model. Two different estimation methods were derived, i.e., maximal likelihood and the moments technique for the DWPLT parameter, and some advanced numerical methods were utilized for the estimation process. A simulation was performed to examine and analyze the performance of the DWPLT estimator on the basis of the criteria of the bias and mean squared errors. The flexibility and fit ability of the proposed distribution is demonstrated via the clinical application of a real dataset. The DWPLT model was more flexible and worked well for modeling real age data when compared to other competitive age distributions in the statistical literature.

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“…The extended version of the Weibull distribution is increasingly becoming an effective tool for modelling lifetime data. The modification is useful in lifetime analysis (reliability analysis), insurance, economy, finance, and engineering (Almazah et al, 2021).…”

Section: Introductionmentioning

confidence: 99%

Simulation Study on Modified Weibull Distribution for Modelling of Investment Return

Abubakar¹,

Sabri²

2021

JST

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The Weibull distribution is one of the most popular statistical models extensively applied to lifetime data analysis such as survival data, reliability data, wind speed, and recently in financial data, due to itsts flexibility to adaptably imitate different families of statistical distributions. This study proposed a modified version of the two-parameter Weibull distribution by incorporating additional parameters in the internal rate of return and insurance claims data. The objective is to examine the behaviour of investment return on the assumption of the proposed model. The proposed and the existing Weibull distribution parameters have been estimated via a simulated annealing algorithm. Experimental simulations have been conducted mimicking the internal rate of return (IRR) data for both short time (small sample) and long-term investment periods (large samples). The performance of the proposed model has been compared with the existing two-parameter Weibull distribution model in terms of their R-square (R2), mean absolute error (MAE), root mean squared error (RMSE), Akaike’s information criterion (AIC), and the Kolmogorov-Smirnov test (KS). The numerical simulation revealed that the proposed model outperformed the existing two-parameter Weibull distribution model in terms of accuracy, robustness, and sensitivity. Therefore, it can be concluded that the proposed model is entirely suitable for the long-term investment period. The study will be extended using the internal rate of return real data set. Furthermore, a comparison of the various Weibull distribution parameter estimators such as metaheuristics or evolutionary algorithms based on the proposed model will be carried out.

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A New Extended Geometric Distribution: Properties, Regression Model, and Actuarial Applications

Cited by 7 publications

References 18 publications

Modified-Lindley distribution and its applications to the real data

Modified-Lindley distribution and its applications to the real data

An Extension of the Poisson Distribution: Features and Application for Medical Data Modeling

Simulation Study on Modified Weibull Distribution for Modelling of Investment Return

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