Bayesian estimation for the mean of delta-gamma distributions with application to rainfall data in Thailand

PeerJ. 2022 May 18:10:e13465. doi: 10.7717/peerj.13465. eCollection 2022.

Abstract

Precipitation and flood forecasting are difficult due to rainfall variability. The mean of a delta-gamma distribution can be used to analyze rainfall data for predicting future rainfall, thereby reducing the risks of future disasters due to excessive or too little rainfall. In this study, we construct credible and highest posterior density (HPD) intervals for the mean and the difference between the means of delta-gamma distributions by using Bayesian methods based on Jeffrey's rule and uniform priors along with a confidence interval based on fiducial quantities. The results of a simulation study indicate that the Bayesian HPD interval based on Jeffrey's rule prior performed well in terms of coverage probability and provided the shortest expected length. Rainfall data from Chiang Mai province, Thailand, are also used to illustrate the efficacies of the proposed methods.

Keywords: Chiang Mai; Credible intervals; Fiducial quantities; Highest posterior density intervals; Jeffrey’s rule; Rainfall data; Simulation; Uniform priors.

Publication types

  • Research Support, Non-U.S. Gov't

MeSH terms

  • Bayes Theorem*
  • Computer Simulation
  • Probability
  • Statistical Distributions
  • Thailand

Grants and funding

This research received financial support from the National Science, Research, and Innovation Fund (NSRF) and King Mongkut’s University of Technology North Bangkok (Grant No. KMUTNB-FF-66-03). The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.