A proposed method to estimate the value of dependency for the copula function

Abstract

Most of life applications consist of several variables, and for such variables, there should be a relation, which in most cases are complicated, and affect each other. We utilize the association function to find a mathematical relationship among those variables. Association function is considered one as non-parametric functions that used to find the common distributions between the variables in order to model the survival function of two variables. In our research, we use three different relations of Gumbel, Clayton, and Archimedean for Rayleigh distribution of one parameter. Using the association function can possibly estimate the harmony and alignment which achieved between among the variables of the study and from using three methods for estimating the harmony values through the correlation between association function and Kendall correlation function for each particular association. Various values for Rayleigh distribution have been tested with different samples and different experiments in order to find the best harmony value  which represents the rate of optimum association, and to find the binomial distribution. After performing the comparisons by using (MSE), the results show that Clayton Association is the best one for all samples. This association has been selected to be implemented for real data which are selected from Babylon Tires Factory in Najaf governorate for a sample of (50) observations of locally manufactured tires for a variable (L), with operating time measured  in minutes (S) for a number of times of speed acceleration where the reliability values have been calculated for each case.