Rama Shanker https://orcid.org/0000-0002-5002-8904 , Umme Habibah Rahman https://orcid.org/0000-0002-6168-6283

(English) PDF


The paper focuses on type II Topp-Leone Frechet distribution. Its properties including hazard rate function, reverse hazard rate function, Mills ratio, quantile function and order statistics have been studied. The maximum likelihood estimation used for estimating the parameters of the proposed distribution has been explained and expressions for the Fisher information matrix and confidence intervals have been provided. The paper discusses the applications of the distribution for modeling several datasets relating to temperature. Finally, the goodness of fit of the proposed distribution has been compared with that of the Frechet distribution.


Frechet distribution, Topp-Leone distribution, reliability properties, applications


Afify, A. Z., Yousof, H. M., Cordeiro, G. M., Ortega, E. M. M., Nofai, Z. M., (2016). The Weibull-Frechet distribution and its application, Journal of Applied Statistics, Vol. 43, Issue. 14, pp. 2608–2626.

Al-Zaharani, B., (2012). Goodness of fit for the Topp-Leone distribution with unknown parameters, Applied Mathematical Sciences, Vol. 6, pp. 6355–6363.

Elgarhy, M., Nasir, M. A., Jamal, F., Ozel, G., (2018). The type II Topp-Leone family of distributions: properties and applications, Journal of Statistics and Management Systems, Vol. 21, No. 8, pp. 1529–1551.

Fréchet, M., (1927). Sur la loi de Probabilité de l'écart Maximum, Annales de la Société Polonaise de Mathematique, Vol.6, pp. 93–116.

Ghitany, M.E., Kotz, S., Xie, M., (2011). On some reliability measures and their stochastic orderings for the Topp-Leone distribution, Journal of Applied Statistics, Vol. 32, No. 7, pp. 715–722.

Gupta, R. D., Kundu, D., (1999). Generalized exponential distributions, Australian and Newzealand Journal of Statistics, Vol. 41, pp. 173–188.

Krishna, E., Jose, K. K., (2013). The Marshall-Olkin Frechet distribution, Communication in Statistics-Theory and Methods ,Vol. 42, No. 22, pp. 4091–4107.

Mahmoud, M. R., Mandouh, R. M., (2013). On the transmuted Frechet distribution, Journal of Applied Sciences Research , Vol. 9, No. 10, pp. 5553–5561.

Mead, M. E., Afify, A. Z., Hamedani, G. G., Ghosh, I., (2017).The Beta Exponential Frechet Distribution with Application, Austrian Journal of Statistics ,Vol. 46, pp. 41–63.

Mubarak, M., (2012). Parameter estimation based on the Frechet progressive type-II censored data with binomial removals, Journal of Quality and Reliability Engineering, pp. 1–5.

Nadarajah, S., Kotz, S., (2003a). The exponentiated Frechet distribution, Interstat Electronic Journal, Vol. 14, pp. 1–7

Nadarajah, S., Kotz, S., (2003b). Moments of some J-shaped distributions, Journal of Applied Statistics , Vol. 30, No. 3, pp. 311–317.

Nadarajah, S., Kotz, S.(2006). The exponentiated type distributions, Acta ApplicaThe exponentiated Frechet distribution, Interstat Electronic Journal, Vol. 14, pp. 1–7.

Nasir, W., Aslam, M., (2015). Bayes approach to study shape parameter of Frechet distribution, International Journal of Basic Applied Science , Vol. 4, No. 3, pp.246–254.

Reyad, H., Mustafa, C. K., Afify, A. Z., Hamedani, G. G.,Othman, S., (2021). The Frechet Topp Leone G-family of distribution: Properties, Characteristics and Application. Annals of Data Science ,Vol. 8, issue, 2, No. 2, pp. 345–366.

Sangsanit, Y., Bodhisuwan, W. (2016). The Topp-Leone generator of distribution: properties and inference, Sangklanankarin Journal of Science and Technologyy, Vol. 38, No. 5, pp. 537–548.

Shanker, R., Shukla, K. K., (2019). A Generalization of Weibull Distribution, Reliability: Theory & Applications, Vol. 14, No.2, pp. 57–70.

Topp, C. W.,Leone, F. C., (1955). A family of J-shaped frequency functions, Journal of American Statistical Association , Vol. 35, No. 10, pp. 1115–1129.

Weibull, W., (1951). A statistical distribution function of wide applicability, Journal of Applied Mechanics ,Vol. 18, pp. 293–297.

Back to top
© 2019–2024 Copyright by Statistics Poland, some rights reserved. Creative Commons Attribution-ShareAlike 4.0 International Public License (CC BY-SA 4.0) Creative Commons — Attribution-ShareAlike 4.0 International — CC BY-SA 4.0