Main Article Content

Abstract

In this article, we propose a new four-parameter Fréchet distribution called the odd Lomax Fréchet distribution. The new model can be expressed as a linear mixture of Fréchet densities. We provide some of its mathematical properties. The estimation of the model parameters is performed by the maximum likelihood method. We illustrate the good performance of the maximum likelihood estimates via a detailed numerical simulation study. The importance and usefulness of the proposed distribution for modeling data are illustrated using two real data applications.

Keywords

Fréchet distribution Maximum likelihood estimation Odd Lomax-G class Order statistics

Article Details

How to Cite
Hamed, M., Aldossary, F., & Afify, A. Z. (2020). The four-parameter Fréchet distribution: Properties and applications. Pakistan Journal of Statistics and Operation Research, 16(2), 249-264. https://doi.org/10.18187/pjsor.v16i2.3097

References

  1. Abouelmagd, T. H. M., Hamed, M. S., Afify, A. Z., Al-Mofleh, H. and Iqbal, Z. (2018). The Burr X Fréchet distribution with its properties and applications. Journal of Applied Probability and Statistics, 13, 23-51.
  2. Afify, A. Z., Hamedani, G. G., Ghosh, I. and Mead, M. E. (2015). The transmuted Marshall-Olkin Fréchet distribution: properties and applications. International Journal of Statistics and Probability, 4, 132-184.
  3. Afify, A. Z., Yousof, H. M., Cordeiro, G. M. Ortega, E. M. M. and Nofal, Z. M. (2016) The Weibull Fréchet distribution and its applications. Journal of Applied Statistics, 43, 2608-2626.
  4. Choulakian, V. and Stephens, M. (2001). Goodness-of-Fit tests for the generalized Pareto distribution. Technometrics, 43, 478-484.
  5. Cordeiro, G. M., Afify, A. Z., Ortega, E. M., Suzuki, A. K. and Mead, M. E. (2019). The odd Lomax generator of distributions: properties, estimation and applications. Journal of Computational and Applied Mathematics, 347, 222-237.
  6. Fréchet M. (1924). Sur la loi des erreurs dIobservation. Bulletin de la Société Mathématique de Moscou, 33, 5-8.
  7. Krishna, E., Jose, K. K., Alice, T. and Ristic, M. M. (2013). The Marshall-Olkin Fréchet distribution. Communications in Statistics-Theory and Methods, 42, 4091-4107.
  8. Kotz, S. and Nadarajah, S. (2000). Extreme value distributions: theory and applications. Imperial College Press, London.
  9. Lee, E. T. and Wang, J. W. (2003). Statistical Methods for Survival Data Analysis, 3rd edn. Wiley, New York.
  10. Mahmoud, M. R. and Mandouh, R. M. (2013). On the transmuted Fréchet distribution. Journal of Applied Sciences Research, 9, 5553-5561.
  11. Mansour, M. M., Abd Elrazik, E. M., Altun, E., Afify, A. Z. and Iqbal, Z. (2018a). A new three-parameter Fréchet distribution: properties and applications. Pak. J. Statist, 34, 441-458.
  12. Mansour, M. M., Aryal, G., Afify, A. Z. and Ahmad, M. (2018b). The kumaraswamy exponentiated Fréchet distribution. Pak. J. Statist, 34, 177-193.
  13. Mead, M. E. and Abd-Eltawab A. R. (2014). A note on Kumaraswamy Fréchet distribution. Australian Journal of Basic and Applied Sciences, 8, 294-300.
  14. Mead, M. E., Afify, A. Z., Hamedani, G. G. and Ghosh, I. (2017). The beta exponential Fréchet distribution with applications. Austrian Journal of Statistics, 46, 41-63.
  15. Mubarak, M. (2011). Parameter estimation based on the Fréchet progressive type II censored data with binomial removals. Journal of Quality, Statistics and Reliability 2012 (2011).
  16. Nadarajah, S. and Gupta, A. K. (2004). The beta Fréchet distribution. Far East Journal of Theoretical Statistics, 14, 15-24.
  17. Nadarajah, S. and Kotz, S. (2003). The exponentiated Fréchet distribution. Interstat Electronic Journal, 1-7.
  18. Ramos, P. L., Louzada, F., Ramos, E. and Dey, S. (2019). The Fréchet distribution: estimation and application-an overview. Journal of Statistics and Management Systems, 1-30.
  19. Ramos, P. L., Nascimento, D. and Louzada, F. (2017). The Long Term Fréchet Distribution: Estimation, Properties and Its Application. Biom. Biostat. Int. J., 6, 357-362.
  20. Silva, R. V. D., de Andrade, T. A., Maciel, D., Campos, R. P. and Cordeiro, G. M. (2013). A new lifetime model: the gamma extended Fréchet distribution. Journal of Statistical Theory and Applications, 12, 39-54.
  21. Tablada, C. J. and Cordeiro, G. M. (2017). The modified Fréchet distribution and its properties. Communications in Statistics-Theory and Methods, 46, 10617-10639.