The first part of this paper reviews the properties of bivariate dependence measures as Spearman’s rho and Kendall’s tau under the different copula. The second part of this paper derives the bivariate inverted Topp-Leone (BITL) distribution based on Farlie- Gumbel-Morgenstern (FGM), Ali-Mikhail-Haq (AMH), Plackett, and Clayton copula. The reliability function obtained for bivariate ITL distributions based on copula. The maximum likelihood estimation method for the parameters of the four bivariate ITL distributions has been discussed. Asymptotic confidence intervals for the model parameters are also considered. To evaluate the performance of the models, a Monte Carlo simulation study is conducted to compare the efficiency between the four models. Also, a medical real data set of diabetic nephropathy is analyzed to investigate the models and useful results are obtained for illustrative purposes. Anderson–Darling- type statistic and Crame ́r–von Mises statistic for copula goodness-of-fit testing are obtained.
Z. Muhammed, Hiba; A. El-Sherpieny, El-Sayed; and M. Almetwally, Ehab
"Dependency Measures For New Bivariate Models Based on Copula Function,"
Information Sciences Letters: Vol. 10
, Article 15.
Available at: https://digitalcommons.aaru.edu.jo/isl/vol10/iss3/15