IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v10y2022i24p4724-d1001029.html
   My bibliography  Save this article

Simultaneous Confidence Intervals for the Ratios of the Means of Zero-Inflated Gamma Distributions and Its Application

Author

Listed:
  • Theerapong Kaewprasert

    (Department of Applied Statistics, Faculty of Applied Science, King Mongkut’s University of Technology North Bangkok, Bangkok 10800, Thailand)

  • Sa-Aat Niwitpong

    (Department of Applied Statistics, Faculty of Applied Science, King Mongkut’s University of Technology North Bangkok, Bangkok 10800, Thailand)

  • Suparat Niwitpong

    (Department of Applied Statistics, Faculty of Applied Science, King Mongkut’s University of Technology North Bangkok, Bangkok 10800, Thailand)

Abstract

Heavy rain in September (the middle of the rainy season in Thailand) can cause unexpected events and natural disasters such as flooding in many areas of the country. Rainfall series that contain both zero and positive values belong to the zero-inflated gamma distribution, which combines the binomial and gamma distributions. Precipitation in various areas of a country can be estimated by using simultaneous confidence intervals (CIs) for the ratios of the means of multiple zero-inflated gamma populations. Herein, we propose six simultaneous CIs constructed using the fiducial generalized CI method, Bayesian and highest posterior density (HPD) interval methods based on the Jeffreys’rule or uniform prior, and method of variance estimates recovery (MOVER). The performances of the proposed simultaneous CI methods were evaluated using a Monte Carlo simulation in terms of the coverage probabilities and expected lengths. The results from a comparative simulation study show that the HPD interval based on the Jeffreys’rule prior performed the best in most cases, while in some situations, the fiducial generalized CI performed well. All of the methods were applied to estimate the simultaneous CIs for the ratios of the means of natural rainfall data from six regions in Thailand.

Suggested Citation

  • Theerapong Kaewprasert & Sa-Aat Niwitpong & Suparat Niwitpong, 2022. "Simultaneous Confidence Intervals for the Ratios of the Means of Zero-Inflated Gamma Distributions and Its Application," Mathematics, MDPI, vol. 10(24), pages 1-22, December.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:24:p:4724-:d:1001029
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/10/24/4724/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/10/24/4724/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Patcharee Maneerat & Pisit Nakjai & Sa-Aat Niwitpong, 2022. "Bayesian interval estimations for the mean of delta-three parameter lognormal distribution with application to heavy rainfall data," PLOS ONE, Public Library of Science, vol. 17(4), pages 1-25, April.
    2. Kalimuthu Krishnamoorthy & Xiao Wang, 2016. "Fiducial confidence limits and prediction limits for a gamma distribution: Censored and uncensored cases," Environmetrics, John Wiley & Sons, Ltd., vol. 27(8), pages 479-493, December.
    3. Jan Hannig & Thomas C. M. Lee, 2009. "Generalized fiducial inference for wavelet regression," Biometrika, Biometrika Trust, vol. 96(4), pages 847-860.
    4. Hannig, Jan & Iyer, Hari & Patterson, Paul, 2006. "Fiducial Generalized Confidence Intervals," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 254-269, March.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Li, Xinmin & Wang, Juan & Liang, Hua, 2011. "Comparison of several means: A fiducial based approach," Computational Statistics & Data Analysis, Elsevier, vol. 55(5), pages 1993-2002, May.
    2. Russell J. Bowater, 2017. "A defence of subjective fiducial inference," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 101(2), pages 177-197, April.
    3. Hannig, Jan & Lai, Randy C.S. & Lee, Thomas C.M., 2014. "Computational issues of generalized fiducial inference," Computational Statistics & Data Analysis, Elsevier, vol. 71(C), pages 849-858.
    4. Hsin-I Lee & Hungyen Chen & Hirohisa Kishino & Chen-Tuo Liao, 2016. "A Reference Population-Based Conformance Proportion," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 21(4), pages 684-697, December.
    5. Weizhong Tian & Yaoting Yang & Tingting Tong, 2022. "Confidence Intervals Based on the Difference of Medians for Independent Log-Normal Distributions," Mathematics, MDPI, vol. 10(16), pages 1-14, August.
    6. Shin-Fu Tsai, 2019. "Comparing Coefficients Across Subpopulations in Gaussian Mixture Regression Models," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 24(4), pages 610-633, December.
    7. David R. Bickel, 2014. "Small-scale Inference: Empirical Bayes and Confidence Methods for as Few as a Single Comparison," International Statistical Review, International Statistical Institute, vol. 82(3), pages 457-476, December.
    8. Yixuan Zou & Jan Hannig & Derek S. Young, 2021. "Generalized fiducial inference on the mean of zero-inflated Poisson and Poisson hurdle models," Journal of Statistical Distributions and Applications, Springer, vol. 8(1), pages 1-15, December.
    9. Xiong, Shifeng, 2011. "An asymptotics look at the generalized inference," Journal of Multivariate Analysis, Elsevier, vol. 102(2), pages 336-348, February.
    10. Li, Xinmin & Zhou, Xiaohua & Tian, Lili, 2013. "Interval estimation for the mean of lognormal data with excess zeros," Statistics & Probability Letters, Elsevier, vol. 83(11), pages 2447-2453.
    11. Roy, Anindya & Bose, Arup, 2009. "Coverage of generalized confidence intervals," Journal of Multivariate Analysis, Elsevier, vol. 100(7), pages 1384-1397, August.
    12. Yuliang Yin & Bingbing Wang, 2016. "The Agreement between the Generalized Value and Bayesian Evidence in the One-Sided Testing Problem," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2016, pages 1-7, May.
    13. Piero Veronese & Eugenio Melilli, 2021. "Confidence Distribution for the Ability Parameter of the Rasch Model," Psychometrika, Springer;The Psychometric Society, vol. 86(1), pages 131-166, March.
    14. A. Malekzadeh & M. Kharrati-Kopaei & S. Sadooghi-Alvandi, 2014. "Comparing exponential location parameters with several controls under heteroscedasticity," Computational Statistics, Springer, vol. 29(5), pages 1083-1094, October.
    15. Veronese, Piero & Melilli, Eugenio, 2018. "Some asymptotic results for fiducial and confidence distributions," Statistics & Probability Letters, Elsevier, vol. 134(C), pages 98-105.
    16. Friedrich, Thomas & Knapp, Guido, 2013. "Generalised interval estimation in the random effects meta regression model," Computational Statistics & Data Analysis, Elsevier, vol. 64(C), pages 165-179.
    17. Piao Chen & Zhi‐Sheng Ye & Xun Xiao, 2019. "Pairwise model discrimination with applications in lifetime distributions and degradation processes," Naval Research Logistics (NRL), John Wiley & Sons, vol. 66(8), pages 675-686, December.
    18. CHEN, Piao & YE, Zhi-Sheng, 2018. "A systematic look at the gamma process capability indices," European Journal of Operational Research, Elsevier, vol. 265(2), pages 589-597.
    19. Shin‐Fu Tsai, 2020. "Approximate two‐sided tolerance intervals for normal mixture distributions," Australian & New Zealand Journal of Statistics, Australian Statistical Publishing Association Inc., vol. 62(3), pages 367-382, September.
    20. Yang Liu & Jan Hannig, 2017. "Generalized Fiducial Inference for Logistic Graded Response Models," Psychometrika, Springer;The Psychometric Society, vol. 82(4), pages 1097-1125, December.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:10:y:2022:i:24:p:4724-:d:1001029. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.