Comparing particulate matter dispersion in Thailand using the Bayesian Confidence Intervals for ratio of coefficients of variation

Abstract

Recently, harmful levels of air pollution have been detected in many provinces of Thailand. Particulate matter (PM) contains microscopic solids or liquid droplets that are so small that they can be inhaled and cause serious health problems. A high dispersion of PM is measured by a coefficient of variation of log-normal distribution. Since the log-normal distribution is often used to analyse environmental data such as hazardous dust particle levels and daily rainfall data. These data focus the statistical inference on the coefficient of variation. In this paper, we develop confidence interval estimation for the ratio of coefficients of variation of two log-normal distributions constructed using the Bayesian approach. These confidence intervals were then compared with the existing approaches: method of variance estimates recovery (MOVER), modified MOVER, and approximate fiducial approaches using their coverage probabilities and average lengths via Monte Carlo simulation. The simulation results show that the Bayesian confidence interval performed better than the others in terms of coverage probability and average length. The proposed approach and the existing approaches are illustrated using examples from data set PM10 level and PM2.5 level in the northern Thailand.

Bayesian Confidence Intervals for Coefficients of Variation of PM10 Dispersion

“…For the difference between the coefficients of variation of log-normal distributions, the three classical confidence intervals: MOVER by using the variance of Nam and Kwon [11], modified MOVER by using the Chi-squared approach of Niwitpong [21], and the approximate fiducial approach with modified normal-based approximations were compared with the Bayesian confidence interval. The results in this investigation were similar to those of Harvey and van der Merwe [7], Rao and D'Cunha [9], Thangjai and Niwitpong [14], and Thangjai et al [22].…”

“…Rao and D'Cunha [9] proposed a novel approach to obtain inference using the median of a log-normal distribution. Thangjai et al [10], Nam and Kwon [11], Hasan and Krishnamoorthy [12], Niwitpong et al [13], Thangjai and Niwitpong [14], and Thangjai et al [15] suggested confidence intervals for functions of the coefficient of variation of a log-normal distribution. Furthermore, Thangjai and Niwitpong [16,17] introduced approaches to estimate the confidence intervals for functions of the signal-to-noise ratio of log-normal distributions.…”

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

“…The FGCI and Bayesian approaches were derived using a simulation technique whereas the adjusted MOVER approach was derived using formulas. The results in this investigation are similar to those of Harvey & van der Merwe (2012) ; Rao & D’Cunha (2016) , Thangjai & Niwitpong (2020b) , Thangjai, Niwitpong & Niwitpong (2021a) and Thangjai, Niwitpong & Niwitpong (2021b) .…”

Estimation of the percentile of Birnbaum-Saunders distribution and its application to PM2.5 in Northern Thailand

“…PM2.5, also known as particulate matter 2.5, refers to tiny particles or droplets suspended in the air with a size not exceeding 2.5 micrometers. These minute particles fall under the category of airborne pollutants and can be composed of a variety of materials, including dust, soil, soot, smoke, and liquid droplets ( Thangjai & Niwitpong, 2020 ). Due to their diminutive size, PM2.5 particles can be readily inhaled into the respiratory system, penetrating deeply.…”