Determination of the Confidence Intervals for Multimodal Probability Density Functions

Abstract

The shortest interval approach can be solved as an optimization problem, while the equallytailed approach is determined by using the distribution function. The equal density approach isproposed instead of the optimization problem for determining the shortest confidence interval. Itis applied to multimodal probability density functions to determine the shortest confidenceinterval. Furthermore, the equal density and optimization approach for the shortest confidenceinterval and the equally tailed approach were applied to numerical examples and their resultswere compared. Nevertheless, the main subject of this study is the calculation of the shortestconfidence intervals for any multimodal distribution.