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.
Highlights
In statistics, a con...dence interval is an estimation of a parameter which represents the population within an acceptable range
The results show that the con...dence region is found no matter how complex the distribution function
Sidak [6] proved the validity of the rectangular con...dence regions for the means of multivariate normal distributions given by Dunn [3, 4]
Summary
A con...dence interval is an estimation of a parameter which represents the population within an acceptable range. Dunn [3, 4] presented several procedures for determining the rectangular con...dence regions. Chew [5] compiled the formulas for con...dence, prediction, and tolerance regions for the multivariate normal distribution for the various cases of known and unknown mean vector and covariance matrix. Sidak [6] proved the validity of the rectangular con...dence regions for the means of multivariate normal distributions given by Dunn [3, 4]. Hu and Yang [7] proposed a distribution-free approach, based on a few basic geometrical principles, to determine the con...dence region for two or more variables.
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