Estimation of common percentile of rainfall datasets in Thailand using delta-lognormal distributions

Abstract

Weighted percentiles in many areas can be used to investigate the overall trend in a particular context. In this article, the confidence intervals for the common percentile are constructed to estimate rainfall in Thailand. The confidence interval for the common percentile help to indicate intensity of rainfall. Herein, four new approaches for estimating confidence intervals for the common percentile of several delta-lognormal distributions are presented: the fiducial generalized confidence interval, the adjusted method of variance estimates recovery, and two Bayesian approaches using fiducial quantity and approximate fiducial distribution. The Monte Carlo simulation was used to evaluate the coverage probabilities and average lengths via the R statistical program. The proposed confidence intervals are compared in terms of their coverage probabilities and average lengths, and the results of a comparative study based on these metrics indicate that one of the Bayesian confidence intervals is better than the others. The efficacies of the approaches are also illustrated by applying them to daily rainfall datasets from various regions in Thailand.

Confidence Intervals for Mean and Difference between Means of Delta-Lognormal Distributions Based on Left-Censored Data

“…The BS approach is recommended for constructing credible intervals for the mean and the difference between means of DLN distributions containing left-censored data. This result is consistent with those reported by Thangjai et al [17,31]. Additionally, the GCI approach can be used to estimate the confidence intervals for the difference between means of DLN distributions based on left-censored data, which is similar to the findings reported by Thangjai and Niwitpong [10] and Thangjai et al [28].…”

“…Step 2: Compute µ|σ 2 , y from Equation (17) Step 3: Compute ω BS from Equation (18) Step 4: Repeat Step 1-Step 3 a total m times and obtain an array of ω BS 's…”

“…Moreover, several researchers have proposed confidence intervals for various functions of the DLN distribution, such as the mean, coefficient of variation, and percentile. For instance, Maneerat et al [14], Maneerat et al [15], Yosboonruang et al [16], and Thangjai et al [17] have all explored this topic.…”

Simultaneous Confidence Intervals for Ratios of the Percentiles of the Delta-Lognormal Distribution

“…Thus, the FGCI method builds upon the foundation of FGPQs. In accordance with Thangjai et al [8], let i p be the percentiles and…”

“…In this simulation study, we conducted a performance comparison of four methods, which are denoted as FGCI, HPD.J, HPD.JR, and HPD.U, as described in equations ( 4), ( 6), (7), and (8), respectively. This comparison was carried out using the statistical software R through Monte Carlo simulations.…”