International Journal of Advanced and Applied Sciences

Int. j. adv. appl. sci.

EISSN: 2313-3724

Print ISSN: 2313-626X

Volume 4, Issue 7  (July 2017), Pages:  66-73

Title:  A bivariate exponentiated Pareto distribution derived from Gaussian copula

Author(s):  Ashwag S. Al-Urwi, Lamya A. Baharith *


Department of Statistics, Faculty of Science, King Abdulaziz University, Jeddah, Saudi Arabia

Full Text - PDF          XML


The exponentiated Pareto distribution has been used quite effectively to model many lifetime data. In this paper, a new bivariate exponentiated Pareto distribution is introduced. The proposed bivariate distribution is derived from Gaussian copula with exponentiated Pareto distribution as marginals. Some properties of the bivariate exponentiated Pareto distribution can be obtained using the Gaussian copula property. Moreover, several methods of estimation are considered to estimate the unknown parameters of the proposed bivariate distribution. Numerical simulations are carried out to compare the performances of different estimators.  Finally, one real data is analyzed and the results showed that the proposed bivariate distribution is useful for real life applications. 

© 2017 The Authors. Published by IASE.

This is an open access article under the CC BY-NC-ND license (

Keywords: Exponentiated Pareto distribution, Gaussian copula, Maximum likelihood estimators, Inference functions for margins estimators, Canonical maximum likelihood estimators, Bayesian estimators

Article History: Received 25 March 2017, Received in revised form 4 May 2017, Accepted 10 May 2017

Digital Object Identifier:


Al-Urwi AS and Baharith LA (2017). A bivariate exponentiated Pareto distribution derived from Gaussian copula. International Journal of Advanced and Applied Sciences, 4(7): 66-73


Achcar JA, Moala FA, Tarumoto MH, and Coladello LF (2015). A bivariate generalized exponential distribution derived from copula functions in the presence of censored data and covariates. Pesquisa Operacional, 35(1): 165-186.
AL-Hussaini EK and Ateya SF (2006). A class of multivariate distributions and new copulas. Journal of the Egyptian Mathematical Society, 14(1): 45-54.
Al-Mutairi D, Ghitany M, and Kundu D (2011). A new bivariate distribution with weighted exponential marginals and its multivariate generalization. Statistical Papers, 52(4): 921-936.
Balakrishnan N and Lai CD (2009). Continuous bivariate distributions. Springer Science and Business Media, Berlin, Germany.
EL-Damcese M, Mustafa A, and Eliwa M (2015). Bivariate exponentiated generalized weibull-gompertz distribution. arXiv preprint arXiv:1501.02241. Available online at:
El-Gohary A and El-Morshedy M (2015). Bivariate Exponentiated Modified Weibull Extension. arXiv preprint arXiv:1501.03528 Available online at:
El-Sherpieny E, Ibrahim S, and Bedar RE (2013). A new bivariate distribution with generalized gompertz marginals. Asian Journal of Applied Sciences, 1(04): 141-150.
Freund JE (1961). A bivariate extension of the exponential distribution. Journal of the American statistical Association, 56(296): 971-977.
Genest C, Ghoudi K, and Rivest LP (1995). A semiparametric estimation procedure of dependence parameters in multivariate families of distributions. Biometrika, 82(3): 543-552.
Genest C, Rémillard B, and Beaudoin D (2009). Goodness-of-fit tests for copulas: A review and a power study. Insurance: Mathematics and economics, 44(2): 199-213.
Gupta RC, Gupta PL, and Gupta RD (1998). Modeling failure time data by Lehman alternatives. Communications in Statistics-Theory and methods, 27(4): 887-904.
Gupta RC, Kirmani S, and Srivastava H (2010). Local dependence functions for some families of bivariate distributions and total positivity. Applied Mathematics and Computation, 216(4): 1267-1279.
Hutchinson TP and Lai CD (1990). Continuous bivariate distributions, emphasising applications. Rumsby Scientific Publishing, Adelaide, Australia.
Joe H and Xu JJ (1996). The estimation method of inference function for margins for multivariate models. Technical Report 166, University of British Columbia, Vancouver, Canada.
Kundu D (2015). Bivariate sinh-normal distribution and a related model. Brazilian Journal of Probability and Statistics, 29(3): 590-607.
Kundu D and Gupta RD (2011). Absolute continuous bivariate generalized exponential distribution. Advances in Statistical Analysis, 95(2): 169-185.
Kundu D, Balakrishnan N, and Jamalizadeh A (2010). Bivariate birnbaum–saunders distribution and associated inference. Journal of Multivariate Analysis, 101(1): 113-125.
Mardia KV (1970). Families of bivariate distributions. Griffin publishing, Spokane, Washington, USA.
Marshall AW and Olkin I (1967). A generalized bivariate exponential distribution. Journal of Applied Probability, 4(02): 291-302.
Nelsen RB (2007). An introduction to copulas. Springer Science and Business Media, Berlin, Germany.
Olkin I and Trikalinos TA (2015). Constructions for a bivariate beta distribution. Statistics and Probability Letters, 96: 54-60.
Quiroz-Flores A (2009). Testing copula functions as a method to derive bivariate weibull distributions. APSA 2009 Toronto Meeting Paper. Available online at:
Sankaran P, Nair NU, and John P (2014). A family of bivariate Pareto distributions. Statistica, 74(2): 199-215.
Sarhan AM and Balakrishnan N (2007). A new class of bivariate distributions and its mixture. Journal of Multivariate Analysis, 98(7): 1508-1527.
Shawky AI and Abu-Zinadah HH (2009). Exponentiated pareto distribution: different method of estimations. International Journal of Contemporary Mathematical Sciences, 4(14): 677-693.
Sklar M (1959). Fonctions de répartition à n dimensions et leurs marges. University of Paris, Paris, France.
Trivedi PK and Zimmer DM (2007). Copula modeling: an introduction for practitioners. Foundations and Trends in Econometrics, now Publishers Inc., Boston, USA.
Whitt W (1976). Bivariate distributions with given marginals. The Annals of Statistics, 4(6): 1280-1289.