No abstract

The modified goodness of fit tests for the Rayleigh distribution are studied. The critical values of modified Kolmogorov-Smirnov, Cramer-von-Mises and Anderson-Darling tests are obtained by Monte Carlo simulation for different sample sizes and significant levels. The type I error rate and power of these tests are studied and compared. The results show that all of the three tests have type I error rate close to the significant levels. Under several alternative distributions, it is founded that when the sample size is large, modified Anderson-Darling has the largest power in all cases. However, when the sample size is small, skewness of the distribution plays an important role. For the more skewed distribution, the modified Anderson-Darling test has more power than the others, while the modified Cramer-von-Mises has the largest power when the distribution is less skewed.

The fine particulate matter (PM2.5) concentrations is one of the most important issues that are often discussed since it has a greater impact on human health. Statistical distribution modeling plays an important role in predicting PM2.5 concentrations. This research aims to find the optimum statistical distribution model of PM2.5 in Rayong Province and Chonburi Province. The daily average data from 2014 – 2019 for Rayong and from 2015 – 2019 for Chonburi were using. Five statistical distributions were compared. A proper statistical distribution that represents PM2.5 concentrations has been chosen based on three criteria include Anderson-Darling statistic and RMSE. The results show that Pearson type VI distribution performs better compared to other distributions for PM2.5 concentrations in Rayong. For Chonburi, the proper statistical distribution is Log normal distribution.