A New Generalization of the Exponentiated Fréchet Distribution with Applications
DOI:
https://doi.org/10.13052/jrss0974-8024.1516Keywords:
Alpha Power Exponentiated Fréchet, Exponentiated Fréchet Distribution, entropy, momentAbstract
The addition of an extra parameter to standard distributions is a common technique in statistical theory. This study introduces a new generalization of the Exponentiated Fréchet distribution named alpha power exponentiated Fréchet distribution (APEF). The APEF allows for a significant amount of versatility in modeling various data forms as it accommodates upside-down bathtubs, decreasing, and reversed-J shapes for hazard rate function. Some of the APEF’s mathematical properties are derived in close forms. The maximum likelihood technique is used to estimate the new distribution parameters. Numerical results are calculated to demonstrate the estimators’ performance. Five well-known real-life applications show the flexibility and potentiality of the APEF empirically. The APEF outperforms other competing distributions based on model selection criteria.
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Afify, A., Yousof, H., Cordeiro, G., Ortega, E. & Nofal, Z. The Weibull Fréchet distribution and its applications. Journal of Applied Statistics. 43, 2608–2626, 2016.
Al-Marzouki, S., Jamal, F., Chesneau, C. & Elgarhy, M. Type II Topp Leone power Lomax distribution with applications. Mathematics. 8(4), 2020.
Almetwally, E., Alharbi, R., Alnagar, D. & Hafez, E. A New Inverted Topp-Leone Distribution: Applications to the COVID-19 Mortality Rate in Two Different Countries. Axioms. 10(25), 2021.
Alotaibi, R., Khalifa, M., Baharith, L., Dey, S. & Rezk, H. The Mixture of the Marshall–Olkin Extended Weibull Distribution under Type-II Censoring and Different Loss Functions. Mathematical Problems in Engineering, 2021.
Alzaatreh, A. & Ghosh, I. On the Weibull-X family of distributions. Journal of Statistical Theory and Applications. 14, 169–183, 2015.
Alzaatreh, A., Lee, C. & Famoye, F. A new method for generating families of continuous distributions. Metron. 71, 63–79, 2013.
Baharith, L. & Aljuhani, W. New Method for Generating New Families of Distributions. Symmetry. 13(4), pp. 726, 2021.
Baharith, L. & Alamoudi, H. The Exponentiated Fréchet Generator of Distributions with Applications. Symmetry. 13(4), pp. 572, 2021.
Barreto-Souza, W., Cordeiro, G. & Simas, A. Some results for beta Fréchet distribution. Communications in Statistics-Theory and Methods. 40, 798–811, 2011.
Bourguignon, M., Silva, R. & Cordeiro, G. The Weibull-G family of probability distributions. Journal of Data Science. 12, 53–68, 2014.
Ceren, Ü., Cakmakyapan, S. & Gamze, Ö. Alpha power inverted exponential distribution: Properties and application. Gazi University Journal of Science. 31, 954–965, 2018.
Coles, S., Bawa, J., Trenner, L. & Dorazio, P. An introduction to statistical modeling of extreme values. Springer, 2001.
Cordeiro, G. & Castro, M. A new family of generalized distributions. Journal of Statistical Computation and Simulation. 81, 883–898, 2011.
Dey, S., Ghosh, I. & Kumar, D. Alpha-power transformed Lindley distribution: properties and associated inference with application to earthquake data. Annals of Data Science. 6, 623–650, 2019.
Eghwerido, J. The alpha power Weibull Frechet distribution: properties and applications. Turkish Journal of Science. 5, 170–185, 2020.
Eghwerido, J., Nzei, L. & Agu, F. The alpha power Gompertz distribution: characterization, properties, and applications. Sankhya A. 1–27, 2020.
Elbatal, I., Asha, G. & Raja, A. transmuted exponentiated Fréchet distribution: properties and applications. Journal of Statistics Applications & Probability. 3, pp. 379, 2014.
Eugene, N., Lee, C. & Famoye, F. Beta-normal distribution and its applications. Communications in Statistics-Theory and Methods. 31, 497–512, 2002.
Haq, M. & Elgarhy, M. The odd Fréchet-G family of probability distributions. Journal of Statistics Applications & Probability. 7, 189–203, 2018.
Ihtisham, S., Khalil, A., Manzoor, S., Khan, S. & Ali, A. Alpha-Power Pareto distribution: Its properties and applications. PloS One. 14, 6:e0218027, 2019.
Keller, A., Kamath, A. & Perera, U. Reliability analysis of CNC machine tools. Reliability Engineering. 3, 449–473 , 1982.
Klakattawi, H. & Aljuhani, W. A New Technique for Generating Distributions Based on a Combination of Two Techniques: Alpha Power Transformation and Exponentiated TX Distributions Family. Symmetry. 13(3), pp. 412, 2021.
Kotz, S. & Nadarajah, S. Extreme value distributions: theory and applications. World Scientific, 2000.
Krishna, E., Jose, K., Alice, T. & Ristić, M. The Marshall-Olkin Fréchet distribution. Communications in Statistics-Theory and Methods. 42, 4091–4107, 2013.
Linhart, H. & Zucchini, W. Model selection. John Wiley & Sons, 1986.
Mahdavi, A. & Kundu, D. A new method for generating distributions with an application to exponential distribution. Communications in Statistics-Theory and Methods. 46, 6543–6557, 2017.
Mead, M. A note on Kumaraswamy Fréchet distribution. Australia. 8, pp. 294–300, 2014.
Nadarajah, S. & Kotz, S. The exponentiated Fréchet distribution. Interstat Electronic Journal. 14, pp. 1–7 , 2003.
Nadarajah, S. & Kotz, S. The exponentiated type distributions. Acta Applicandae Mathematica. 92, 97–111, 2006.
Nasiru, S. Extended odd Fréchet-G family of distributions. Journal of Probability and Statistics, 2018.
Nasiru, S., Mwita, P. & Ngesa, O. Alpha power transformed Frechet distribution. Applied Mathematics & Information Sciences. 13: 129–141, 2019.
Nassar, M., Alzaatreh, A., Mead, M. & Abo-Kasem, O. Alpha power Weibull distribution: Properties and applications. Communications in Statistics-Theory and Methods. 46, 10236–10252, 2017.
Nassar, M., Kumar, D., Dey, S., Cordeiro, G. & Afify, A. The Marshall–Olkin alpha power family of distributions with applications. Journal of Computational And Applied Mathematics. pp. 351, 41–53, 2019.
Reyad, H., Korkmaz, M., Afify, A., Hamedani, G. & Othman, S. The Fréchet Topp Leone-G family of distributions: Properties, characterizations and applications. Annals Of Data Science. 8(2), 345–366, 2021.
Pillai, J. & Moolath, G. A New Generalization of the Fréchet Distribution: Properties and Application. Statistica. 79, 267–289, 2019.
Riffi, M., Ansari, S. & Hamdan, M. A generalized transmuted Frechet distribution. J. Stat. Appl. Pro. 7, 1–10, 2019.
Silva, R., Andrade, T., Maciel, D., Campos, R. & Cordeiro, G. A new lifetime model: The gamma extended Fréchet distribution. Journal of Statistical Theory and Applications. 12, 39–54, 2013.
Tahir, M., Cordeiro, G., Alizadeh, M., Mansoor, M., Zubair, M. & Hamedani, G. The odd generalized exponential family of distributions with applications. Journal of Statistical Distributions and Applications. 2(1), 2015.
Tahir, M., Hussain, M., Cordeiro, G., El-Morshedy, M. & Eliwa, M. A new Kumaraswamy generalized family of distributions with properties, applications, and bivariate extension. Mathematics. 8(11), pp. 1989, 2020
Team, R. & Others R: A language and environment for statistical computing. Vienna, Austria, 2013.
Yang, Y., Tian, W. & Tong, T. Generalized Mixtures of Exponential Distribution and Associated Inference. Mathematics. 9(12), pp. 1371, 2021.
ZeinEldin, R., Haq, M., Hashmi, S. & Elsehety, M. Alpha power transformed inverse Lomax distribution with different methods of estimation and applications. Complexity, 2020.
