A bivariate exponentiated Pareto distribution derived from Gaussian copula

Abstract

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.

New Bivariate Pareto Type II Models

“…The American football league data obtained from the matches played on three consecutive weekends in 1986 have two variables T 1 and T 2 where; T 1 is the game time the first fields scored when the ball kicks between goalposts and T 2 is the game time the first touchdown is scored, see [41]. The histogram and the scatter plots of T 1 and T 2 are right skewed and positively correlated [29]. The sample Spearman correlation coefficient between T 1 and T 2 is 0.804 which allows using the proposed BPII distribution to model this bivariate data.…”

“…The plots of the fitted and the empirical CDF for the two marginals based on ML estimates are illustrated in Figure 2 Hence, the K-S test along with the plots of the fitted and the empirical CDF in Figure 2 indicate that the BPII distribution has an appropriate fit for this bivariate data. In addition, the Gaussian copula is appropriate for this data as indicated in [29]. For more details, see [43].…”

“…This indicates that BPIImG distribution is more appropriate for this data. The model's comparison illustrated in [29] is re-conducted to compare BPIIG and BPIImG with Bivariate expatiated Pareto derived from the mixture and Gaussian copula (BEPmG), bivariate exponentiated generalized Weibull-Gompertz distribution (BEGWG) studied by [44], and bivariate exponentiated Gompertez distribution (BEG) using the same real data set.…”

“…In addition, the dependence property of the copula method between random variables gives researchers a general structure to model multivariate distributions [23,24]. Several studies have lately introduced bivariate distributions using copula and some of these have derived by combining the mixture and copula methods [25][26][27][28][29][30][31][32].…”