Determination of the Confidence Intervals for Multimodal Probability Density Functions

Year 2018, Volume: 31 Issue: 1, 310 - 326, 01.03.2018

ORHAN Kesemen , BUĞRA Tiryaki , EDA Özkul , ÖZGE Tezel

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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