Constructions for a bivariate beta distribution

A New Method for Generating Continuous Bivariate Distribution Families

Recently, it has been observed that a new method for generating continuous distributions, T - X family, can be quite effectively used to analyze the data in one dimension. The aim of this study is to generalize this method to two dimensional space so that the marginals would have T - X distributions. So, several examples and properties of this family have been presented. As ...

Reliability For A Bivariate Gamma Distribution

In the area of stress-strength models there has been a large amount of work as regards estimation of the reliability R = Pr(X < Y ). The algebraic form for R = Pr(X < Y ) has been worked out for the vast majority of the well-known distributions when X and Y are independent random variables belonging to the same univariate family. In this paper, we consider forms of R when (X,Y ) follow a bivari...

Reliability for Some Bivariate Beta Distributions

In the area of stress-strength models there has been a large amount of work as regards estimation of the reliability R = Pr(X < Y). The algebraic form for R = Pr(X < Y) has been worked out for the vast majority of the well-known distributions when X and Y are independent random variables belonging to the same univariate family. In this paper, we consider forms of R when (X ,Y) follows a bivaria...

The Bivariate Marginal Distribution

The Bivariate Normal Distribution

Let U and V be two independent normal random variables, and consider two new random variables X and Y of the form X = aU + bV, Y = cU + dV, where a, b, c, d, are some scalars. Each one of the random variables X and Y is normal, since it is a linear function of independent normal random variables.† Furthermore, because X and Y are linear functions of the same two independent normal random variab...