Advances and Applications in Statistics

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BIVARIATE WEIBULL FRÉCHET MODEL BASED ON GAUSSIAN COPULA

Authors

  • Sulafah M. Saleh Binhimd

Keywords:

Weibull distribution, Fréchet distribution, Gaussian copula, bivariate Weibull Fréchet distribution, parametric and semi-parametric estimation methods.

DOI:

https://doi.org/10.17654/0972361725027

Abstract

The Weibull distribution has been used effectively in many fields, especially for lifetime applications such as engineering, biomedical, and social sciences, among others. It is a continuous probability distribution that is used to examine product reliability, model failure rates, and analyze life data. The Fréchet distribution can be contrasted to the inverse Weibull distribution. In this paper, a bivariate model of the Weibull and Fréchet distributions is proposed due to its importance with lifetime applications. The proposed model is based on Gaussian copula, which is utilized in many applications as an emerging model. The inference about the new model is discussed through semi-parametric and parametric techniques. Finally, the successful performance of the suggested distribution is next examined using the goodness of fit test, and methods of inference are illustrated.

Received: October 25, 2024
Revised: January 9, 2025
Accepted: January 18, 2025

References

M. K. Abd Elaal, Bivariate beta exponential distributions, International Organization of Scientific Research Journal of Mathematics 13(3) (2017), 7-19. doi:10.9790/5728-1303010719.

M. K. Abd Elaal and L. A. Baharth, Bivariate Rayleigh distribution with application, International Journal of Electronics Communication and Computer Engineering 8(3) (2017), 156-159. doi:10.13140/RG.2.2.26089.54886.

S. A. Adham, M. K. Abd Elaal and H. M. Malaka, Gaussian copula regression application, Int. Math. Forum 11(22) (2016), 1053-1065.

S. A. Adham and S. G. Walker, A multivariate Gompertz-type distribution, J. Appl. Stat. 28(8) (2001), 1051-1065. doi:10.1080/02664760120076706.

G. R. AL-Dayian, S. A. Adham, S. H. El Beltagy and M. K. Abd Elaal, Bivariate half-logistic distribution based on mixture and copula, Academy of Business Journal 2 (2008), 92-107.

E. K. AL-Hussaini and S. F. Ateya, A class of multivariate distributions and new copulas, J. Egyptian Math. Soc. 14(1) (2006), 45-54.

A. Alzaatreh, F. Famoye and C. Lee, Weibull-Pareto distribution and its applications, Comm. Statist. Theory Methods 42(9) (2013a), 1673-1691. doi:10.1080/03610926.2011.599002.

M. Bourguignon, R. B. Silva and G. M. Cordeiro, The Weibull-G family of probability distributions, Journal of Data Science 12(1) (2014), 53-68.

doi:10.6339/JDS.2014.12(1).1210.

L. A. Baharith and A. S. Al-Urwi, A bivariate exponentiated Pareto distribution derived from Gaussian copula, International Journal of Advanced and Applied Sciences 4(7) (2017), 66-73. doi:10.21833/ijaas.2017.07.010.

G. M. Cordeiro, A. E. Gomes, C. Q. da-Silva and E. M. Ortega, The beta exponentiated Weibull distribution, J. Stat. Comput. Simul. 83(1) (2013), 114-138.

G. M. Cordeiro, R. R. Pescim and E. M. M. Ortega, The Kumaraswamy generalized half-normal distribution for skewed positive data, Journal of Data Science 10(2) (2012), 195-224. doi:10.6336/JDS.2012.10(2).1010.

J. Dobric and F. Schmid, A goodness of fit test for copulas based on Rosenblatt’s transformation, Comput. Statist. Data Anal. 51(9) (2007), 4633-4642. doi:10.1016/j.csda.2006.08.012.

N. Eugene, C. Lee and F. Famoye, Beta-normal distribution and its applications, Comm. Statist. Theory Methods 31(4) (2002), 497-512.

doi: 10.1081/STA-120003130.

J. D. Fermanian, Goodness-of-fit tests for copulas, J. Multivariate Anal. 95(1) (2005), 119-152. doi:10.1016/j.jmva.2004.07.004.

C. Genest and B. Remillard, Validity of the parametric bootstrap for goodness of fit testing in semiparametric models, Ann. Inst. Henri Poincare Probab. Stat. 44(6) (2008), 1096-1127. doi:10.1214/07-AIHP148.

C. Genest, B. Remillard and D. Beaudoin, Goodness of fit test for copulas: a review and a power study, Insurance Math. Econom. 44(2) (2009), 199-213. doi:10.1016/j.insmatheco.2007.10.005.

C. Genest, K. Ghudi and P. Rivest, A semiparametric estimation procedure of dependence parameters in multivariate families of distributions, Biometrika 82(3) (1995), 543-552. doi:10.1093/biomet/82.3.543.

Z. I. Kalantan and M. K. Abd Elaal, Parameters estimations on bivariate Weibull G distributions: a new family, Advances and Applications in Statistics 58(2) (2019), 77-122. doi:10.17654/AS08020077.

Z. I. Kalantan and M. K. Abd Elaal, A new family based on lifetime distribution: bivariate Weibull-G models based on Gaussian copula, International Journal of Advanced and Applied Sciences 5(12) (2018), 100-111.

doi:10.21833/ijaas.2018.12.012.

I. Kojadinovic and J. Yan, Comparison of three semiparametric methods for estimating dependence parameters in copula models, Insurance Math. Econom. 47(1) (2010), 52-63. doi:10.1016/j.insmatheco.2010.03.008.

I. Kojadinovic, J. Yan and M. Holmes, Fast large-sample goodness of fit tests for copulas, Statist. Sinica 21(2) (2011), 841-871. doi:10.5705/ss.2011.037a.

D. Kundu, Bivariate Sinh-normal distribution and a related model, Braz. J. Probab. Stat. 29(3) (2015), 590-607. doi:10.1214/13-BJPS235.

D. Kundu, N. Balakrishnan and A. Jamalizadeh, Bivariate Birnbaum-Saunders distribution and associated inference, J. Multivariate Anal. 101(1) (2010), 113-125. doi:10.1016/j.jmva.2009.05.005.

D. Kundu and R. D. Gupta, Absolute continuous bivariate generalized exponential distribution, AStA Advances in Statistical Analysis 95(2) (2011), 169-185.

doi:10.1007/s10182-010-0151-0.

R. B. Nelsen, An Introduction to Copulas, Springer Series in Statistics, New York, Inc., 1999.

M. M. Ristic and N. Balakrishnan, The gamma-exponentiated exponential distribution, J. Stat. Comput. Simul. 82(2) (2012), 1191-1206.

doi:10.1080/00949655.2011.574633.

M. Sklar, Fonctions de repartition a n dimensions et leurs marges, Publ. Inst. Statist. Univ. Paris 8(1) (1959), 229-231.

P. K. Trivedi and D. M. Zimmer, Copula modeling: an introduction for practitioners, Foundations and Trends in Econometrics 1(1) (2005), 1-111.

doi:10.1561/0800000005.

A. F. Jenkinsom, The frequency distribution of the annual maximum (or minimum) values of meteorological elements, Quarterly Journal of the Royal Meteorological Society 81(1) (1955), 158-171. doi:10.1002/qj.49708134804.

S. Kotz and S. Nadarajah, Extreme Value Distributions: Theory and Applications, Word Scientific, Imperial College Press, London, 2000. doi:10.1142/p191.

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Published

08-03-2025

Issue

Vol. 92 No. 5 (2025)

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Articles

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How to Cite

BIVARIATE WEIBULL FRÉCHET MODEL BASED ON GAUSSIAN COPULA. (2025). Advances and Applications in Statistics , 92(5), 663-681. https://doi.org/10.17654/0972361725027

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