Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

# Confidence Interval Estimation for Precipitation Quantiles Based on Principle of Maximum Entropy

Version 1 : Received: 15 January 2019 / Approved: 16 January 2019 / Online: 16 January 2019 (10:11:03 CET)

A peer-reviewed article of this Preprint also exists.

Wei, T.; Song, S. Confidence Interval Estimation for Precipitation Quantiles Based on Principle of Maximum Entropy. Entropy 2019, 21, 315. Wei, T.; Song, S. Confidence Interval Estimation for Precipitation Quantiles Based on Principle of Maximum Entropy. Entropy 2019, 21, 315.

## Abstract

Confidence interval of is an interval corresponding to a specified confidence and including the true value. It can be used to describe the precision of a statistical quantity and quantify its uncertainty. Although the principle of maximum entropy (POME) has been used for a variety of applications in hydrology, the confidence intervals of the POME quantile estimators have not been available. In this study, the calculation formulas of asymptotic variances and confidence intervals of quantiles based on POME for Gamma, Pearson type 3 (P3) and Extreme value type 1 (EV1) distributions were derived. Monte Carlo Simulation experiments were performed to evaluate the performance of derived formulas for finite samples. Using four data sets for annual precipitation at the Weihe River basin in China, the derived formulas were applied for calculating the variances and confidence intervals of precipitation quantiles for different return periods and the results were compared with those of the methods of moments (MOM) and of maximum likelihood (ML) method. It is shown that POME yields the smallest standard errors and the narrowest confidence intervals of quantile estimators among the three methods, and can reduce the uncertainty of quantile estimators

## Keywords

Principle of maximum entropy; quantile estimation; confidence interval; Monte Carlo simulation; precipitation frequency analysis

## Subject

Engineering, Control and Systems Engineering

Views 0
Metrics 0