Confidence regions for bivariate probability density functions using polygonal areas

Abstract

In this study, a polygonal approach is suggested to generalize the

notion of the condence region of the univariate probability density function

for the bivariate probability density function. The equal density approach is

used to demonstrate that condence regions can be polygonal shapes. The bisection

method is the preferred method in nding the equal density value that

reveals the desired condence coecient. Condence regions estimate not only

bivariate unimodal probability functions but also bivariate multimodal probability

functions. An approach is enhanced to estimate these condence regions

for probability density functions which are dened as rectangular, polygonal

and innite expanse areas.

Keywords

• bivariate probability density functions,Bivariate confidence region,multimodal confidence region,polygonal confidence region

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