Statistics and Its Interface

Volume 14 (2021)

Number 3

Bayesian confidence intervals for variance of delta-lognormal distribution with an application to rainfall dispersion

Pages: 229 – 241

DOI: https://dx.doi.org/10.4310/20-SII630

Authors

Patcharee Maneerat (Department of Mathematics, Uttaradit Rajabhat University, Uttaradit, Thailand)

Suparat Niwitpong (Department of Applied Statistics, King Mongkut’s University of Technology North Bangkok, Bangkok, Thailand)

Sa-Aat Niwitpong (Department of Applied Statistics, King Mongkut’s University of Technology North Bangkok, Bangkok, Thailand)

Abstract

For climate studies in agriculture, rainfall records often involve data which contain zeros and highly non-zero skewness. This is mostly used in models for prediction or that use the mean for approximation. Rainfall dispersion is also important in evaluations as it can vary enormously, and it is a natural phenomenon which can lead to drought or flood. Herein, the goal of this paper is to propose a variational approximation computed with interval estimator based on Bayesian approach for delta-lognormal variance consisting of the highest posterior density interval based on vague prior (HPD-V) and the method of variance estimates recovery (MOVER). By way of comparison, the performances of these intervals were evaluated in terms of coverage probability and relative average length via a Monte Carlo simulation. The numerical results show that HPD-V was much more likely to outperform the other methods in many situations even large variance, although MOVER became the recommended method when both of variance and the probability of having zero were small. Our methods were then be utilized to analyze the variability in Nan province’s daily rainfall dataset in a comparison with the other methods.

Keywords

agriculture, Bayesian approach, MOVER, natural rainfall, vague prior, variance

Full Text (PDF format)

Received 24 January 2020

Accepted 29 July 2020

Published 9 February 2021