SavedAdd your journal

Journals / Hacettepe Journal of Mathematics and Statistics / 2017 / Cilt: 46 - Sayı: 4

Generalized transmuted family of distributions: properties and applications

G.G. HAMEDANİ
Morad ALİZADEH
Faton MEROVCİ
Pages
645–667
Publication Date
2022-10-18
DOI
—
🏛️Bibliographic metadata and full text access for this article are provided via DergiPark.
DergiPark Record ↗
✨

AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

Finally certain characterziations of our model are presented.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:We introduce and study general mathematical properties of a new generator of continuous distributions with two extra parameters called theGeneralized Transmuted Family of Distributions.
📊
Key Findings & Data:We discuss the different methods of estimation of the model parameters and illustrate the potential application of the model via real data.
💡
Conclusion & Impact:Finally certain characterziations of our model are presented.
🔬Design:Modeling & Simulation
📍Scope:Comprehensive Sample
⚙️Variables:Transmuted distribution · Generated family · Maximum likelihood

Abstract

We introduce and study general mathematical properties of a new generator of continuous distributions with two extra parameters called theGeneralized Transmuted Family of Distributions. We investigate the shapes and present some special models. The new density function can be expressed as a linear combination of exponentiated densities in terms of the same baseline distribution. We obtain explicit expressions for the ordinary and incomplete moments and generating function, Bonferroni and Lorenz curves, asymptotic distribution of the extreme values, Shannon and Rényi entropies and order statistics, which hold for any baseline model. Further, we introduce a bivariate extension of the new family. We discuss the different methods of estimation of the model parameters and illustrate the potential application of the model via real data. A brief simulation for evaluating Maximum likelihood estimator is done. Finally certain characterziations of our model are presented.

🔖

Cite This Article

HAMEDANİ, G., ALİZADEH, M., MEROVCİ, F. (2022). Generalized transmuted family of distributions: properties and applications. Hacettepe Journal of Mathematics and Statistics, Cilt: 46 - Sayı: 4, 645–667. https://ajindex.com/articles/529922

📄 Full Text PDF Viewer

📄

PDF görüntüleyici hazırlanıyor...

References (10)

  1. Alexander, C., Cordeiro, G. M., Ortega, E. M., & Sarabia, J. M. (2012). Generalized betagenerated distributions. Computational Statistics & Data Analysis, 56(6), 1880-1897.
  2. Alizadeh, M., Cordeiro, G. M., de Brito, E., & Demétrio, C. G. B. (2015). The beta Marshall-Olkin family of distributions. Journal of Statistical Distributions and Applica- tions, 2(1), 1-18.
  3. Alizadeh, M., Emadi, M., Doostparast, M., Cordeiro, G. M., Ortega, E. M., & Pescim, R. R. (2015). A new family of distributions: the Kumaraswamy odd log-logistic, properties and applications. Hacettepe Journal of Mathematics and Statistics (to appear). Alizadeh, M., Tahir, M. H., Cordeiro, G. M., Mansoor, M., Zubair, M., & Hamedani, G. G. (2015). The Kumaraswamy Marshal-Olkin family of distributions. Journal of the Egyptian Mathematical Society. Alzaatreh, A., Lee, C., & Famoye, F. (2013). A new method for generating families of continuous distributions. Metron, 71(1), 63-79.
  4. Alzaghal, A., Famoye, F., & Lee, C. (2013). Exponentiated T-X Family of Distributions with Some Applications. International Journal of Statistics and Probability, 2(3), p31. Amini, M., MirMostafaee, S. M. T. K., Ahmadi, J. (2014). Log-gamma-generated families of distributions. Statistics, 48(4), 913-932.
  5. Andrews, D. F., Herzberg, A. M. (2012). Data: a collection of problems from many elds for the student and research worker. Springer Science Business Media. Aryal, G. R. (2013). Transmuted log-logistic distribution. Journal of Statistics Applications & Probability, 2(1), 11-20.
  6. Aryal, G. R., & Tsokos, C. P. (2009). On the transmuted extreme value distribution with application. Nonlinear Analysis: Theory, Methods & Applications, 71(12), e1401-e1407. Aryal, G. R., & Tsokos, C. P. (2011). TransmutedWeibull Distribution: A Generalization of theWeibull Probability Distribution. European Journal of Pure and Applied Mathematics, 4(2), 89-102.
  7. Bourguignon, M., Silva, R. B., & Cordeiro, G. M. (2014). The WeibullG family of probability distributions. Journal of Data Science, 12(1), 53-68.
  8. Cheng, R. C. H., & Amin, N. A. K. (1983). Estimating parameters in continuous univariate distributions with a shifted origin. Journal of the Royal Statistical Society. Series B (Methodological), 394-403.
  9. Cordeiro, G. M., Alizadeh, M., & Diniz Marinho, P. R. (2015). The type I half-logistic family of distributions. Journal of Statistical Computation and Simulation, (ahead-of-print), 1-22.
  10. Cordeiro, G. M., Alizadeh, M., & Ortega, E. M. (2014). The expone