Derivation of bivariate probability density functions with exponential marginals Academic Article uri icon

abstract

  • A vivariate probability density function (pdf), f(x 1 , x 2 ), admissible for two random variables (X 1 , X 2 ), is of the form {Mathematical expression} where ρ(u, v) (u=F 1 (x 1 ), v=F 2 (x 2 )) is any function on the unit square that is 0-marginal and bounded below by-1 and F 1 (x 1 ) and F 2 (x 2 ) are cumulative distribution functions (cdf) of marginal probability density functions f 1 (x 1 ) and f 2 (x 2 ). The purpose of this study is to determine f(x 1 , x 2 ) for different forms of ρ(u,v). By considering the rainfall intensity and the corresponding depths as dependent random variables, observed and computed probability distributions F 1 (x 1 ), F(x 1 /x 2 ), F 2 (x 2 ), and F(x 2 /x 1 ) are compared for various forms of ρ(u,v). Subsequently, the best form of ρ(u,v) is specified. © 1991 Springer-Verlag.

author list (cited authors)

  • Singh, K., & Singh, V. P.

citation count

  • 78

publication date

  • March 1991