Bayesian confidence intervals for the difference between variances of delta-lognormal distributions.

highest posterior density probability-matching prior rainfall reference prior variance

Journal

Biometrical journal. Biometrische Zeitschrift
ISSN: 1521-4036
Titre abrégé: Biom J
Pays: Germany
ID NLM: 7708048

Informations de publication

Date de publication:
11 2020
Historique:
received: 07 03 2019
revised: 25 03 2020
accepted: 26 03 2020
pubmed: 23 6 2020
medline: 9 9 2021
entrez: 23 6 2020
Statut: ppublish

Résumé

Unnatural rainfall fluctuation can result in such severe natural phenomena as drought and floods. This variability not only occurs in areas with unusual natural features such as land formations and drainage but can also be due to human intervention. Since rainfall data often contain zero values, evaluating rainfall change is an important undertaking, which can be estimated via the confidence intervals for the difference between delta-lognormal variances using the highest posterior density-based reference (HPD-ref) and probability-matching (HPD-pm) priors. Simulation results indicate that HPD-pm performances were better than other methods in terms of coverage rates and relative average lengths for the difference in delta-lognormal variances, even with a large difference in variances. To illustrate the efficacy of our proposed methods, we applied them to daily rainfall data sets for the lower and upper regions of northern Thailand.

Identifiants

pubmed: 32567112
doi: 10.1002/bimj.201900079
doi:

Types de publication

Journal Article Research Support, Non-U.S. Gov't

Langues

eng

Sous-ensembles de citation

IM

Pagination

1769-1790

Subventions

Organisme : Thailand Science Research and Innovation (TSRI) and National Research Council of Thailand (NRCT)
ID : PHD/0198/2561
Pays : International
Organisme : King Mongkut's University of Technology North Bangkok
ID : KMUTNB-61-KNOW-005
Pays : International

Informations de copyright

© 2020 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Références

Aitchison, J. (1955). On the distribution of a positive random variable having a discrete probability mass at the origin. Journal of the American Statistical Association, 50, 901-908.
Aitchison, J., & Brown, J. A. C. (1963). The lognormal distribution: With special reference to its uses in economics. London, UK: Cambridge University Press.
Berger, J. O., & Bernardo, J. M. (1992). On the development of reference priors. Bayesian Statistics, 4, 35-60.
Box, G. E. P., & Tiao, G. C. (1973). Bayesian inference in statistical analysis. New York, NY: Wiley Classics.
Buntao, N., Niwitpong, S.-A., & Kreinovich, V. (2012). Estimating statistical characteristics of lognormal and delta-lognormal distributions under Interval uncertainty: Algorithms and computational complexity. Departmental Technical Report, Department of Computer Science, University of Texas at El Paso, 1-38.
Casella, G., & Berger, R. L. (2002). Statistical inference (2nd ed.). CA: Pacific Grove.
Chen, Y.-H., & Zhou, X.-H. (2006). Generalized confidence intervals for the ratio or difference of two means for lognormal populations with zeros. UW Biostatistics Working Paper Series, 1-16.
Cojbasic, V., & Tomovic, A. (2007). Nonparametric confidence intervals for population variance of one sample and the difference of variances of two samples. Computational Statistics & Data Analysis, 51, 5562-5578.
Datta, G. S., & Ghosh, J. K. (1995). On priors providing frequentist validity for Bayesian inference. Biometrika, 82, 37-45.
Fletcher, D. (2008). Confidence intervals for the mean of the delta-lognormal distribution. Environmental and Ecological Statistics. 15, 175-189.
Gelman, A, Carlin, J. B., Stern, H. S., Dunson, D. B., Vehtari, A., & Rubin, D. B. (2014). Bayesian data analysis. Boca Raton, Florida, United States: Taylor & Francis Group.
Hannig, J., Iyer, H., & Patterson, P. (2006). Fiducial generalized confidence intervals. Journal of the American Statistical Association, 101, 254-269.
Hariraksapitak, P., Sriring, O., & Navaratnam, S. (2018). Landslides in northern Thailand kill seven; houses, roads damaged. Reuters. Retrieved from https://www.reuters.com/article/us-thailand-landslide/landslides-in-northern-thailand-kill-seven-houses-roads-damaged-idUSKBN1KI07T.
Harvey, J., & van der Merwe, A. J. (2012). Bayesian confidence intervals for means and variances of lognormal and bivariate lognormal distributions. Journal of Statistical Planning and Inference, 142, 1294-1309.
Hasan, M. S., & Krishnamoorthy, K. (2018). Confidence intervals for the mean and a percentile based on zero-inflated lognormal data. Journal of Statistical Computation and Simulation, 88, 1499-1514.
Herbert, R. D., Hayen, A., Macaskill, P., & Walter, S. D. (2011). Interval estimation for the difference of two independent variances. Communications in Statistics -Simulation and Computation, 40, 744-758.
Hildreth, C. (1963). Bayesian statisticians and remote clients. Econometrika, 31, 422-438.
Jeffreys, H. (1961). Theory of probability. UK: Oxford University Press.
Krishnamoorthy, K., Lian, X., & Mondal, S. (2011). Tolerance intervals for the distribution of the difference between two independent normal random variables. Communications in Statistics -Theory and Methods, 40, 117-129.
Kruschke, J. K. (2015). Doing Bayesian data analysis: A tutorial with R: JAGS, and Stan (2nd ed.). UK: Elsevier Science.
Li, X., Zhou, X., & Tian, L. (2013). Interval estimation for the mean of lognormal data with excess zeros. Statistics & Probability Letters, 83, 447-2453.
Lo, N. C., Jacobson, L. D., & Squire, J. L. (1992). Indices of relative abundance from fish spotter data based on delta-lognormal models. Canadian Journal of Fisheries and Aquatic Sciences, 49, 2515-2526.
Marks, D. (2011). Climate change and Thailand: impact and response. Contemporary Southeast Asia, 33, 229-258.
Niwitpong, S. (2017). Generalized confidence intervals for function of variances of lognormal distribution. Advances and Applications in Statistics, 51, 151-163.
Owen, W. J., & DeRouen, T. A. (1980). Estimation of the mean for lognormal data containing zeroes and left-censored values, with applications to the measurement of worker exposure to air contaminants. Biometrics, 36, 707-719.
Pennington, M. (1983). Efficient estimators of abundance, for fish and plankton surveys. Biometrics, 39, 281-286.
RStudio Team (2015). RStudio: Integrated development for R. Boston, MA: RStudio, Inc., http://www.rstudio.com/.
Sadooghi-Alvandi, S. M., & Malekzadeh, A. (2014). Simultaneous confidence intervals for ratios of means of several lognormal distributions: A parametric bootstrap approach. Computational Statistics and Data Analysis, 69, 133-140.
Smith, S. J. (1988). Evaluating the efficiency of the delta-distribution mean estimator. Biometrics, 44, 485-493.
Smith, S. J. (1990). Use of statistical models for the estimation of abundance from groundfish trawl survey data. Canadian Journal of Fisheries and Aquatic Sciences, 47, 894-903.
Tian, L. (2005). Inferences on the mean of zero-inflated lognormal data: The generalized variable approach. Statistics in Medicine, 25, 3223-3232.
Tian, L., & Wu, J. (2006). Confidence intervals for the mean of lognormal data with excess zeros. Biometrical Journal, 48, 149-156.
Varinruk, B. (2017). Thailand rice production and rice research and development on climate change. Workshop on strengthening APEC cooperation on food security and climate change, Ha Noi, Viet Nam.
Weerahandi, S. (1993). Generalized confidence intervals. Journal of the American Statistical Association, 88, 899-905.
Welcher, P., & Attaché, A. (2017). Grain and feed update July 2017. Global Agriculture Information Network Report, United States Department of Agriculture - Foreign Agricultural Service.
Wu, W. -H., & Hsieh, H. -N. (2014). Generalized confidence interval estimation for the mean of delta-lognormal distribution: an application to New Zealand trawl survey data. Journal of Applied Statistics, 41, 1471-1485.
Zhou, X. -H., & Tu, W. (1999). Comparison of several independent population means when their samples contain log-normal and possibly zero observations. Biometrics, 55, 645-651.
Zhou, X. H., & Tu, W. (2000). Confidence intervals for the mean of diagnostic test charge data containing zeros. Biometrics, 56, 1118-1125.

Auteurs

Patcharee Maneerat (P)

Department of Applied Statistics, King Mongkut's University of Technology North Bangkok, Bangkok, Thailand.

Sa-Aat Niwitpong (SA)

Department of Applied Statistics, King Mongkut's University of Technology North Bangkok, Bangkok, Thailand.

Suparat Niwitpong (S)

Department of Applied Statistics, King Mongkut's University of Technology North Bangkok, Bangkok, Thailand.

Articles similaires

Prevalence and implications of fragile X premutation screening in Thailand.

Areerat Hnoonual, Sunita Kaewfai, Chanin Limwongse et al.
1.00
Humans Fragile X Mental Retardation Protein Thailand Male Female
Humans Meta-Analysis as Topic Sample Size Models, Statistical Computer Simulation
Humans Algorithms Software Artificial Intelligence Computer Simulation
Humans Robotic Surgical Procedures Clinical Competence Male Female

Classifications MeSH