Confidence Intervals for the Coefficient of Quartile Variation of a Zero-inflated Lognormal Distribution

Yosboonruang, Noppadon; Niwitpong, Sa-Aat

doi:10.28991/esj-2021-01289

Cited by 2 publications

(3 citation statements)

References 34 publications

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“…We extended the FGCI method, as proposed by Yosboonruang et al [24], to handle the construction of the confidence interval for the difference between CQVs in the deltalognormal distribution. Consequently, the parameters of interest, based on Equation (2), are δ i 1 , µ i , and σ i .…”

Section: Fiducial Generalized Confidence Intervalmentioning

confidence: 99%

“…Singh and Usman [23] expanded upon the methods introduced by Ambati et al [17] to estimate the CQV for missing data. Furthermore, Yosboonruang et al [24] developed a confidence interval for the CQV of a zero-inflated lognormal distribution.…”

Section: Introductionmentioning

confidence: 99%

“…In this article, we focus on estimating the dispersion of a dataset that follows a delta-lognormal distribution. One effective method for estimating this dispersion is the CQV, building upon the methodology proposed by Yosboonruang and Niwitpong [24] to examine and compare the dispersion between two datasets. Specifically, we aim to construct the highest posterior density (HPD) and confidence intervals for the difference between the CQVs of two delta-lognormal distributions.…”

Section: Introductionmentioning

confidence: 99%

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Bayesian Estimation for the Difference between Coefficients of Quartile Variation of Delta-Lognormal Distributions: An Application to Rainfall in Thailand

Yosboonruang

Niwitpong

2023

Symmetry

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The coefficient of quartile variation is a valuable measure used to assess data dispersion when it deviates from a normal distribution or displays skewness. In this study, we focus specifically on the delta-lognormal distribution. The lognormal distribution is characterized by its asymmetrical nature and comprises exclusively positive values. However, when these values undergo a logarithmic transformation, they conform to a symmetrical (or normal) distribution. Consequently, this research aims to establish confidence intervals for the difference between coefficients of quartile variation within lognormal distributions incorporating zero values. We employ the Bayesian, generalized confidence interval, and fiducial generalized confidence interval methods to construct these intervals, involving data simulation using RStudio software. We evaluate the performance of these methods based on coverage probabilities and average lengths. Our findings indicate that the Bayesian method, employing Jeffreys’ prior, performs well in low variability, while the generalized confidence interval method is more suitable for higher variability. Therefore, we recommend using both approaches to construct confidence intervals for the difference between the coefficients of the quartile variation in lognormal distributions that include zero values. Furthermore, we apply these methods to rainfall data in Thailand to illustrate their alignment with actual and simulated data.

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Section: Fiducial Generalized Confidence Intervalmentioning

confidence: 99%