The Kumaraswamy Unit-Gompertz Distribution and its Application to Lifetime Datasets

Akata, Innocent U.; Opone, Festus C.; Osagiede, Francis E. U.

doi:10.34198/ejms.11123.122

Cited by 5 publications

(2 citation statements)

References 15 publications

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“…Arshad et al [22] examined this model in the context of dual generalized order statistics. For some recent references, see for example Ahmed and Aftab [23], Akata et al [24] and Alsadat et al [25].…”

Section: Introductionmentioning

confidence: 99%

Statistical Inference for the Unit Gompertz Power Series Distribution Using Ranked Set Sampling with Applications

Yousef,

Hassan,

Almetwally

2024

Assiut University Journal of Multidisciplinary Scientific Resea

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In this article, we present the unit Gompertz-power series distribution class, which is formed by combining the unit Gompertz and power series distributions. This new class of distributions includes some special cases, such as the unit Gompertz binomial, the unit Gompertz Poisson, the unit Gompertz geometric, and the unit Gompertz logarithmic distributions. The new class's mathematical properties, such as quantiles, moments, generating function, order statistics, and Renyi entropy are investigated. The unit Gompertz-power series distribution's sub-models are thoroughly examined.The maximum likelihood and Bayesian methodologies are used to estimate the model parameters for the complete and ranked set sampling. The Bayesian estimation approach under the squared error and linear exponential loss functions is examined. Finally, we demonstrate applications of two real data sets to highlight the adaptability and potential of the one sub-model in the new class of distributions.

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Section: Introductionmentioning

confidence: 99%

Statistical Inference for the Unit Gompertz Power Series Distribution Using Ranked Set Sampling with Applications

Yousef,

Hassan,

Almetwally

2024

Assiut University Journal of Multidisciplinary Scientific Resea

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“…It is, therefore, important to remark that the APTL distribution is the first-lifetime distribution belonging to the alpha power transformed family of distributions that has its support on a unit interval [0, 1]. Other non-nested generalized lifetime distributions with support [0, 1] are found in the works of [21]- [27]. It is hoped that the APTL distribution will be a strong competitor unit distribution in fitting data sets defined on a unit interval.…”

Section: Introductionmentioning

confidence: 99%

The Alpha Power Topp-Leone Distribution: Properties, Simulations and Applications

Ehiwario¹,

Igabari²,

Ezimadu³

2023

JAMP

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This paper presents an extended lifetime probability distribution based on the alpha power transformation. We refer to the proposed distribution as "the Alpha Power Topp-Leone (APTL) distribution". Mathematical properties of the APTL distribution such as the density and cumulative distribution functions, survival and hazard rate functions, quantile function, median, moments and its relative measures, probability weighted moment, moment generating function, Renyi entropy, and the distribution of order statistics were derived. The method of maximum likelihood estimation was employed to estimate the unknown parameters of the APTL distribution. Finally, we used two real data sets obtained from the literature to illustrate the applicability of the APTL distribution in real-life data fitting.

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A novel extended Kumaraswamy distribution and its application to COVID‐19 data

Suleiman,

Daud,

Ishaq

et al. 2024

Engineering Reports

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In the field of biomedical research, data characteristics often exhibit significant variability, challenging the applicability of classical probability distributions for biomedical data modeling. In this research, we introduce a novel four‐parameter distribution called the odd beta prime Kumaraswamy (OBPK) distribution, derived from the odd beta prime generalized family of distributions and the Kumaraswamy distribution. This distribution exhibits greater flexibility compared with the traditional Kumaraswamy distribution. Importantly, the OBPK distribution offers symmetrical, right‐skewed, left‐skewed, bathtub, N‐shaped, J‐shaped, and reversed J‐shaped densities, as well as varied hazard functions, including increasing, decreasing, bathtub, increasing‐decreasing, upside‐down bathtub, and N‐shaped forms. These curvature patterns make it particularly useful for modeling biomedical data. We derive some basic properties of the OBPK distribution. Parameters are estimated using the maximum likelihood approach, and the performance of various estimators is assessed via Monte Carlo simulations. Finally, four applications to real data on COVID‐19 mortality rates from different countries are evaluated to demonstrate the importance of the OBPK model over other extended versions of the Kumaraswamy models. The empirical findings suggest that the OBPK model outperforms other extended versions of the Kumaraswamy models in these applications.

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The Kumaraswamy Unit-Gompertz Distribution and its Application to Lifetime Datasets

Cited by 5 publications

References 15 publications

Statistical Inference for the Unit Gompertz Power Series Distribution Using Ranked Set Sampling with Applications

Statistical Inference for the Unit Gompertz Power Series Distribution Using Ranked Set Sampling with Applications

The Alpha Power Topp-Leone Distribution: Properties, Simulations and Applications

A novel extended Kumaraswamy distribution and its application to COVID‐19 data

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