A Novel Approximation for Computation Bivariate Distribution Functions in Polygonal Area

Abstract

Generally bivariate probability density function defined in a rectangular area is used to calculate the cumulative distribution function from the bivariate probability density function. However, definition limits of the probability density functions being non-rectangular are in existence in practice. In this paper, primarily arbitrary non-rectangular areas are defined by applying a polygonal approach. The polygonal area obtained as a result of this approach constitutes boundaries of the probability density function. Thus, the bivariate piecewise probability density function can be defined in an arbitrary area. Then the cumulative distribution function is calculated in the obtained area. Two types of approaches are used for these calculations. The first approach is applied to take integral analytically of bivariate continuous probability density function in the polygonal area. The second approach is developed a numerical method since the explicit integral of the selected probability density function cannot be found.