Journal of Data Science

Abstract: Correlation coefficients are generally viewed as summaries, causing them to be underutilized. Creating functions from them leads to their use in diverse areas of statistics. Because there are many correlation coefficients (see, for example, Gideon (2007)) this extension makes possible a very broad range of statistical estimators that rivals least squares. The whole area could be called a “Correlation Estimation System.” This paper outlines some of the numerous possibilities for using the system and gives some illustrative examples. Detailed explanations are developed in earlier papers. The formulae to make possible both the estimation and some of the computer coding to implement it are given. This approach has been taken in hopes that this condensed version of the work will make the ideas accessible, show their practicality, and promote further developments.

Abstract: This paper aims to generate multivariate random vector with prescribed correlation matrix by Johnson system. The probability weighted moment (PWM) is employed to assess the parameters of Johnson system. By equat ing the first four PWMs of Johnson system with those of the target distri bution, a system of equations solved for the parameters is established. With suitable initial values, solutions to the equations are obtained by the New ton iteration procedure. To allow for the generation of random vector with prescribed correlation matrix, approaches to accommodate the dependency are put forward. For the four transformation models of Johnson system, nine cases are addressed. Analytical formulae are derived to determine the equivalent correlation coefficient in the standard normal space for six cases, the rest three ones are handled by an interpolation method. Finally, several numerical examples are given out to check the proposed method.