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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
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
Received 24 January 2020
Accepted 29 July 2020
Published 9 February 2021