Extensions of Two Bivariate Strict Archimedean Copulas

Abstract

The copula approach provides an option for capturing the structure of dependence between two quantitative variables. This approach is based on special bivariate functions called copulas. In brief, a copula can be presented as a "functional print" of a structure of dependence. Among the numerous types of copulas, the strict Archimedean copulas are the most famous. However, some of them appear to be unfairly neglected and understudied. We attempt to rehabilitate two of them, namely the Nelsen strict Archimedean copulas numbers 10 and 17 by extending their mathematical functionality. For each of them, the extension is made by the thorough addition of a parameter, which reveals to have a significant impact on several important aspects. As the main results, we determine the range of admissible values for the involved parameters. Then, the basic properties of the proposed extended copulas are studied, including symmetry, tail dependence, bounds, and correlation. A focus is put on the tau of Kendall as the main correlation measure. For one of the extended copulas, it is shown that there are some connections with the Frank copula and that the associated tau of Kendall almost reached the perfect interval of [−1, 1], demonstrating the significance of our findings. Graphics, short statistical works, and numerical tables are given to support the theoretical results.

Bayesian and Non-Bayesian Estimation for the Shape Parameters of New Versions of Bivariate Inverse Weibull Distribution based on Progressive Type II Censoring

“…Figures 7 and 8 show posterior distributions of the four parameters which are symmetric normal. In scheme 2, when m=25, the first recurrence time of the infection period of the kidney can be as follows: 2,7,8,12,13,15,17,22,23,24,34,39,53,96,130,132,141,149,152,185,292,402,447,511,536. The second recurrence time of the Infection period of the kidney can be as follows: 25, 333, 16, 40, 66, 108, 4, 28, 13, 245, 30, 46, 196, 38, 26, 156, 8, 70, 362, 117, 114, 24, 318, 30, 25. In scheme 2, when m=28, the first recurrence time of the Infection period of the kidney can be as follows: 2, 7, 7, 8, 12,13,15,15,17,22,23,24,30,34,39,53,96,130,132,141,149,152,185,292,402,447,511,536.…”

“…In scheme 2, when m=25, the first recurrence time of the infection period of the kidney can be as follows: 2,7,8,12,13,15,17,22,23,24,34,39,53,96,130,132,141,149,152,185,292,402,447,511,536. The second recurrence time of the Infection period of the kidney can be as follows: 25, 333, 16, 40, 66, 108, 4, 28, 13, 245, 30, 46, 196, 38, 26, 156, 8, 70, 362, 117, 114, 24, 318, 30, 25. In scheme 2, when m=28, the first recurrence time of the Infection period of the kidney can be as follows: 2, 7, 7, 8, 12,13,15,15,17,22,23,24,30,34,39,53,96,130,132,141,149,152,185,292,402,447,511,536. The second recurrence time of the Infection period of the kidney can be as follows: 25, 9, 333, 16, 40, 66, 154, 108, 4, 28, 13, 245, 12, 30, 46, 196, 38, 26, 156, 8, 70, 362, 117, 114, 24, 318, 30, 25. Table <...…”

“…We censored the sample forX 1 and X 2 is communicant of X 1 . After generating n sample of bivariate IW (x 1i , x 2[i] )based on Marshall-Olkin method and FGM copula which are discussed in several articles as Muhammed [8], Almetwally and Muhammed [1], Chesneau [12,13], we generate a bivariate censored sample by using these steps:…”

Cambanis-type Bivariate Uniform Distribution: Properties and Moment Estimation

“…[2] studied the concomitants of generalized order statistics and dual generalized order statistics from Cambanis family of bivariate distributions with nonzero parameter values. For some other developments for families of bivariate distributions, see, Thomas and Scaria [25], Koshti [18], Kamalja and Koshti [17], Abd Elgawad et al [1], Husseiny et al [16], El-Sherpieny et al [8], Chacko and George [6], George and Chacko [11], Chesneau [7], Koshti and Kamalja [20], Fayomi et al [9,10] and Haj et al [12]. In this paper, we focus on a specific member of the Cambanis family, the CTBU distribution, and thoroughly investigate its statistical properties.…”