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  2. Vol 5, No 2 (2021)
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Bayesian Confidence Intervals for Coefficients of Variation of PM10 Dispersion

Warisa Thangjai, Sa-Aat Niwitpong, Suparat Niwitpong

Abstract


Herein, we propose the Bayesian approach for constructing the confidence intervals for both the coefficient of variation of a log-normal distribution and the difference between the coefficients of variation of two log-normal distributions. For the first case, the Bayesian approach was compared with large-sample, Chi-squared, and approximate fiducial approaches via Monte Carlo simulation. For the second case, the Bayesian approach was compared with the method of variance estimates recovery (MOVER), modified MOVER, and approximate fiducial approaches using Monte Carlo simulation. The results show that the Bayesian approach provided the best approach for constructing the confidence intervals for both the coefficient of variation of a log-normal distribution and the difference between the coefficients of variation of two log-normal distributions. To illustrate the performances of the confidence limit construction approaches with real data, they were applied to analyze real PM10 datasets from the Nan and Chiang Mai provinces in Thailand, the results of which are in agreement with the simulation results.

 

Doi: 10.28991/esj-2021-01264

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Keywords


Bayesian Approach; Coefficient of Variation; Difference; Log-normal Distribution; Monte Carlo Simulation.

References


Royston, P. “The Lognormal Distribution as a Model for Survival Time in Cancer, With an Emphasis on Prognostic Factors.” Statistica Neerlandica 55, no. 1 (March 2001): 89–104. doi:10.1111/1467-9574.00158.

Lacey, L. F., O. N. Keene, J. F. Pritchard, and A. Bye. “Common Noncompartmental Pharmacokinetic Variables: Are They Normally or Log-Normally Distributed?” Journal of Biopharmaceutical Statistics 7, no. 1 (January 1, 1997): 171–178. doi:10.1080/10543409708835177.

Sharma, Mohita Anand, and Jai Bhagwan Singh. "Use of probability distribution in rainfall analysis." New York Science Journal 3, no. 9 (2010): 40-49.

Krishnamoorthy, K, and Thomas Mathew. “Inferences on the Means of Lognormal Distributions Using Generalized p-Values and Generalized Confidence Intervals.” Journal of Statistical Planning and Inference 115, no. 1 (July 2003): 103–121. doi:10.1016/s0378-3758(02)00153-2.

Hannig, Jan, E. Lidong, Amany Abdel-Karim, and Hari Iyer. "Simultaneous fiducial generalized confidence intervals for ratios of means of lognormal distributions." Austrian Journal of Statistics 35, no. 2&3 (2006): 261-269.

Tian, Lili, and Jianrong Wu. “Inferences on the Common Mean of Several Log-Normal Populations: The Generalized Variable Approach.” Biometrical Journal 49, no. 6 (June 2007): 944–951. doi:10.1002/bimj.200710391.

Harvey, J., and A.J. van der Merwe. “Bayesian Confidence Intervals for Means and Variances of Lognormal and Bivariate Lognormal Distributions.” Journal of Statistical Planning and Inference 142, no. 6 (June 2012): 1294–1309. doi:10.1016/j.jspi.2011.12.006.

Lin, S. H., and R. S. Wang. “Modified Method on the Means for Several Log-Normal Distributions.” Journal of Applied Statistics 40, no. 1 (November 5, 2012): 194–208. doi:10.1080/02664763.2012.740622.

Rao, K. Aruna, and Juliet Gratia D’Cunha. “Bayesian Inference for Median of the Lognormal Distribution.” Journal of Modern Applied Statistical Methods 15, no. 2 (November 1, 2016): 526–535. doi:10.22237/jmasm/1478003400.

Thangjai, Warisa, Sa-Aat Niwitpong, and Suparat Niwitpong. “Simultaneous Fiducial Generalized Confidence Intervals for All Differences of Coefficients of Variation of Log-Normal Distributions.” Integrated Uncertainty in Knowledge Modelling and Decision Making (2016): 552–561. doi:10.1007/978-3-319-49046-5_47.

Nam, Jun-mo, and Deukwoo Kwon. “Inference on the Ratio of Two Coefficients of Variation of Two Lognormal Distributions.” Communications in Statistics - Theory and Methods 46, no. 17 (May 17, 2017): 8575–8587. doi:10.1080/03610926.2016.1185118.

Hasan, Md Sazib, and K. Krishnamoorthy. “Improved Confidence Intervals for the Ratio of Coefficients of Variation of Two Lognormal Distributions.” Journal of Statistical Theory and Applications 16, no. 3 (2017): 345. doi:10.2991/jsta.2017.16.3.6.

Niwitpong, Sa-aat, Suparat Niwitpong, and Warisa Thangjai. “Simultaneous Confidence Intervals for All Differences of Coefficients of Variation of Log-Normal Distributions.” Hacettepe Journal of Mathematics and Statistics (December 31, 2019): 1–17. doi:10.15672/hujms.454804.

Thangjai, Warisa, and Suparat Niwitpong. “Comparing Particulate Matter Dispersion in Thailand Using the Bayesian Confidence Intervals for Ratio of Coefficients of Variation.” Statistics in Transition New Series 21, no. 5 (2020): 41–60. doi:10.21307/stattrans-2020-054.

Thangjai, Warisa, Sa-Aat Niwitpong, and Suparat Niwitpong. “Confidence Intervals for the Common Coefficient of Variation of Rainfall in Thailand.” PeerJ 8 (September 21, 2020): e10004. doi:10.7717/peerj.10004.

Thangjai, Warisa, and Sa-Aat Niwitpong. “Confidence Intervals for the Signal-to-Noise Ratio and Difference of Signal-to-Noise Ratios of Log-Normal Distributions.” Stats 2, no. 1 (February 27, 2019): 164–173. doi:10.3390/stats2010012.

Thangjai, Warisa, and Sa-Aat Niwitpong. “Confidence Intervals for Common Signal-to-Noise Ratio of Several Log-Normal Distributions.” Iranian Journal of Science and Technology, Transactions A: Science 44, no. 1 (November 19, 2019): 99–107. doi:10.1007/s40995-019-00793-3.

Tsim, Y.L., Yip, S.P., Tsang, K.S., Li, K.F. and Wong, H.F. “Haematogoy and Serology.” Annual Report, Honk Kong Medical Technology Association Quality Assurance Programme, (1991): 25-40.

Faupel-Badger, Jessica M., Barbara J. Fuhrman, Xia Xu, Roni T. Falk, Larry K. Keefer, Timothy D. Veenstra, Robert N. Hoover, and Regina G. Ziegler. “Comparison of Liquid Chromatography-Tandem Mass Spectrometry, RIA, and ELISA Methods for Measurement of Urinary Estrogens.” Cancer Epidemiology Biomarkers & Prevention 19, no. 1 (January 2010): 292–300. doi:10.1158/1055-9965.epi-09-0643.

Lipfert, F.W. “Air Pollution and Community Health: A Critical Review and Data Sourcebook.” Van Nostrand Reinhold, New York, USA (1994).

Niwitpong, Sa-aat. “Confidence Intervals for Coefficient of Variation of Lognormal Distribution with Restricted Parameter Space.” Applied Mathematical Sciences 7 (2013): 3805–3810. doi:10.12988/ams.2013.35251.

Thangjai, Warisa, Sa-Aat Niwitpong, and Suparat Niwitpong. “A Bayesian Approach for Estimation of Coefficients of Variation of Normal Distributions.” Sains Malaysiana 50, no. 1 (January 31, 2021): 261–278. doi:10.17576/jsm-2021-5001-25.

Ng, C. K. "Inference on the common coefficient of variation when populations are lognormal: a simulation-based approach." Journal of Statistics: Advances in Theory and Applications 11, no. 2 (2014): 117-134.

Casella, G. and Berger, R.L. “Statistical Inference.” Duxbury, California, USA (2002).

Donner, Allan, and GY Zou. “Closed-Form Confidence Intervals for Functions of the Normal Mean and Standard Deviation.” Statistical Methods in Medical Research 21, no. 4 (September 8, 2010): 347–359. doi:10.1177/0962280210383082.

Krishnamoorthy, K. “Modified Normal-Based Approximation to the Percentiles of Linear Combination of Independent Random Variables with Applications.” Communications in Statistics - Simulation and Computation 45, no. 7 (June 23, 2014): 2428–2444. doi:10.1080/03610918.2014.904342.


Full Text: PDF

DOI: 10.28991/esj-2021-01264

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