Finding the Best Statistical Distribution Model in PM10 Concentration Modeling by using Lognormal Distribution

Abstract The paper presents the results of research aimed at verifying the hypothesis that the Weibull distribution is an appropriate statistical distribution model of microseismicity emission characteristics, namely: energy of phenomena and inter-event time. It is understood that the emission under consideration is induced by the natural rock mass fracturing. Because the recorded emission contain noise, therefore, it is subjected to an appropriate filtering. The study has been conducted using the method of statistical verification of null hypothesis that the Weibull distribution fits the empirical cumulative distribution function. As the model describing the cumulative distribution function is given in an analytical form, its verification may be performed using the Kolmogorov-Smirnov goodness-of-fit test. Interpretations by means of probabilistic methods require specifying the correct model describing the statistical distribution of data. Because in these methods measurement data are not used directly, but their statistical distributions, e.g., in the method based on the hazard analysis, or in that that uses maximum value statistics.

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An estimation method for rain attenuation distribution in microwave multirelay links–compound lognormal distribution model

Electronics and Communications in Japan (Part I Communications) ◽

10.1002/ecja.4410680309 ◽

1985 ◽

Vol 68 (3) ◽

pp. 75-82

Author(s):

Kazuo Morita, Regular Member

Keyword(s):

Lognormal Distribution ◽

Estimation Method ◽

Rain Attenuation ◽

Distribution Model

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Inverse problem for aerosol particle size distribution using SPSO associated with multi-lognormal distribution model

Atmospheric Environment ◽

10.1016/j.atmosenv.2011.06.010 ◽

2011 ◽

Vol 45 (28) ◽

pp. 4892-4897 ◽

Cited By ~ 28

Author(s):

Yuan Yuan ◽

Hong-Liang Yi ◽

Yong Shuai ◽

Bin Liu ◽

He-Ping Tan

Keyword(s):

Inverse Problem ◽

Particle Size ◽

Particle Size Distribution ◽

Size Distribution ◽

Aerosol Particle ◽

Lognormal Distribution ◽

Distribution Model ◽

Aerosol Particle Size

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A Damage Constitutive Model of Rock Subjected to Freeze-Thaw Cycles Based on Lognormal Distribution

Advances in Civil Engineering ◽

10.1155/2021/6658915 ◽

2021 ◽

Vol 2021 ◽

pp. 1-8

Author(s):

Hang Lin ◽

Linyuan Liang ◽

Yifan Chen ◽

Rihong Cao

Keyword(s):

Mechanical Properties ◽

Constitutive Model ◽

Lognormal Distribution ◽

Constitutive Models ◽

Strain Curve ◽

Statistical Distribution ◽

Freeze Thaw ◽

Accurate Quantitative Analysis ◽

Distribution Parameters ◽

Damage Constitutive Model

The constitutive model of rock is closely connected with the mechanical properties of rock. To achieve a more accurate quantitative analysis of the mechanical properties of rock after the action of freeze-thaw cycles, it is necessary to establish the constitutive models of rock subjected to freeze-thaw cycles from the view of rock damage. Based on the assumption of rock couple damage, this study established a statistical damage constitutive model of rock subjected to freeze-thaw cycles by combining the lognormal distribution, which is commonly used in engineering reliability analysis, and the strain strength theory. Then, the coordinates and derivative at the peak of the stress-strain curve of the rock after the action of freeze-thaw cycles were obtained through experiments to solve the statistical distribution parameters με and S of the model, whereafter, the theoretical curves by the established model were compared with the experimental curves to verify the validity of it, which shows a great agreement. Finally, the sensitivity analysis of the statistical distribution parameters was implemented. The results indicate that με reflects the strength of the rock, which shows a positive relation, and S stands for the brittleness of the rock, which shows a negative relation.

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The Statistical Distributions of PM2.5 in Rayong and Chonburi Provinces, Thailand

Asian Journal of Applied Sciences ◽

10.24203/ajas.v8i3.6153 ◽

2020 ◽

Vol 8 (3) ◽

Author(s):

Vanida Pongsakchat ◽

Pattaraporn Kidpholjaroen

Keyword(s):

Fine Particulate Matter ◽

Statistical Distribution ◽

Distribution Model ◽

Statistical Distributions ◽

Average Data ◽

Fine Particulate ◽

Pearson Type ◽

Anderson Darling ◽

Log Normal ◽

Log Normal Distribution

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.

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