Determination of the Confidence Intervals for Multimodal Probability Density Functions

Abstract

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

Keywords

• Multimodal probability density function,Confidence interval estimators,The shortest confidence interval,The equally tailed confidence interval,The equal density confidence interval

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