The Poisson-G Family of Distributions with Applications

Abouelmagd, T. H. M.; Hamed, M. S.; Ebraheim, Abd El Hadi N.

doi:10.18187/pjsor.v13i2.1740

Cited by 8 publications

(3 citation statements)

References 3 publications

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“…These distributions have gained application to real life situations in engineering, health, finance, education, environmental sciences, economics, e.t.c. Examples of families of distribution include Beta-G ( [14]), Weibull-G ( [9]), Poisson-G ( [1]), Exponentiated-G ( [16]),Transmuted-G ( [26]), Cubic Transmuted-G ( [18]), Exponentiated Chen-G ( [7]) to mention a few. With these generated families of distributions, researchers have been enabled to develop new distributions.…”

Section: Introductionmentioning

confidence: 99%

Statistical properties and applications of the modified beta weibull family of distributions to engineering data

Awodutire,

Sule

2024

IFS

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In this work, a new family of distribution, which generalizes the Beta Weibull-G family by the introduction of a shape parameter to enhance better fit and flexibility, called the Modified Beta Weibull-G family of distributions is obtained. The mixture representation of the derived family of distributions was discussed, with the results effective in studying moments, moment generating functions, order statistics. Parameters of the family of distributions were estimated using the maximum likelihood estimation method. By utilizing this modified class of distributions, we build a new distribution called the modified beta Weibull Weibull and applied it to engineering datasets. Application revealed a better performance in model fit, compared to some other distributions.

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Section: Introductionmentioning

confidence: 99%

Statistical properties and applications of the modified beta weibull family of distributions to engineering data

Awodutire,

Sule

2024

IFS

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“…The new families were established using a variety of ways that included adding extra location, scale, shape, and transmuted characteristics. Some of the newly proposed families are the Chen-G family by Anzagra et al [ 6 ], the sine Topp-Leone-G family by Al-Babtain et al [ 4 ], the Poisson-G family by Abouelmagd et al [ 1 ], and the odd Lomax trigonometric generalized family of distributions by Alshanbari et al [ 5 ] etc. Recently, Klakattawi et al [ 15 ] proposed the Marshall–Olkin Weibull generated family.…”

Section: Introductionmentioning

confidence: 99%

Generalization of the Lindley distribution with application to COVID-19 data

Rajitha

Akhilnath

2022

Int J Data Sci Anal

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Creating new distributions with more desired and flexible qualities for modeling lifetime data has resulted in a concentrated effort to modify or generalize existing distributions. In this paper, we propose a new distribution called the power exponentiated Lindley (PEL) distribution by generalizing the Lindley distribution using the power exponentiated family of distributions, that can fit lifetime data. Then the main statistical properties such as survival function, hazard function, reverse hazard function, moments, quantile function, stochastic ordering, MRL, order statistics, etc., of the newly proposed distribution have been derived. The parameters of the distribution are estimated using the MLE method. Then, a Monte Carlo simulation study is used to check the consistency of the parameters of the PEL distribution in terms of MSE, RMSE, and bias. Finally, we implement the PEL distribution as a statistical lifetime model for the COVID-19 case fatality ratio (in %) in China and India, and the new cases of COVID-19 reported in Delhi. Then we check whether the new distribution fits the data sets better than existing well-known distributions. Different statistical measures such as the value of the log-likelihood function, K-S statistic, AIC, BIC, HQIC, and p -value are used to assess the accuracy of the model. The suggested model seems to be superior to its base model and other well-known and related models when applied to the COVID-19 data set.

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“…Over the last decade, several probability distributions have been commonly used in real data modelling and forecasts in applied science, engineering, actuarial science, economics, telecommunications, life testing, and others many areas (Abouelmagd et al, 2017;Garrido et al, 2016;Soliman, et al 2017). In literature, some familiar distribution has been derived, which are used in real data analysis in different areas are: Generalized Exponential-Poisson by Barreto-Souza & Cribari-Neto (2009), Gemotric exponential Poission G by Nadarajah et al (2013), Exponentiated exponential Poisson G family by Ristić & Nadarajah (2014), Kumaraswamy Poisson-G Family by Ramos et al (2015), Exponentiated generalized-G Poisson family by Aryal et al (2017), Poission exponential -G family by Rayad et al (2020), and others.…”

Section: Introductionmentioning

confidence: 99%

A New Poisson Inverted Exponential Distribution: Model, Properties and Application

Dhungana

2020

Prithvi Acad. J.

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A new Poisson Inverted Exponential distribution is developed from the Poisson family of distribution, which has two parameters. The characteristic of the intended model is unimodal, positive skewed and platykurtic, while the characteristic of the hazard function is the inverted bathtub and the decreasing order. Explicit expression of quantile function, moments (including incomplete and conditional moments), moment generating function, residual life function, R`enyi and q-entropies, probability weighted moment and order statistics of the intended model. The value of unknown parameters is estimated by the maximum likelihood estimate with the confidence interval. Similarly, purposed model compared with well-known other five distributions through different criteria like as goodness of fit, P-P plot, Q-Q plots and K-S test. Likewise, we fitted the PDF and CDF of purposed model with other models, it is clear that intended model is great flexibility and satisfactory fit than those models. Therefore purposed model is more useful in real data and life time data analysis and modelling.

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The Poisson-G Family of Distributions with Applications

Cited by 8 publications

References 3 publications

Statistical properties and applications of the modified beta weibull family of distributions to engineering data

Statistical properties and applications of the modified beta weibull family of distributions to engineering data

Generalization of the Lindley distribution with application to COVID-19 data

A New Poisson Inverted Exponential Distribution: Model, Properties and Application

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