[go: up one dir, main page]
Skip to main content
SpringerLink
Log in

Confidence Interval Estimation for the Mean of Zero-Inflated Birnbaum–Saunders Distribution

  • Published:
Lobachevskii Journal of Mathematics Aims and scope Submit manuscript

Abstract

The relationship between wind speed and PM\({}_{2.5}\) is inversely proportional, indicating that higher wind speeds enhance the dispersion of PM\({}_{2.5}\). In other words, when the wind speed increases, especially during strong winds, it leads to improved removal of PM\({}_{2.5}\) concentrations from the environment. The mean of the delta-Birnbaum–Saunders distribution can be used to analyze wind speed data for predicting future wind speeds. In this study, we construct generalized confidence interval (GCI), bootstrap confidence interval (BCI) and generalized fiducial confidence interval (GFCI) based on the variance estabilized transformation (VST), Wlison, and Hannig methods. The results of a Monte Carlo simulation study indicate that the coverage probabilities of the generalized confidence interval and the generalized fiducial confidence interval based on VST method are greater than or close to the nominal confidence level of 0.95 and provide the shortest averaged length. The average lengths of the proposed confidence intervals tended to decrease when the sample size increased. Wind speed data from Chiang Rai province, Thailand, was used to illustrate the efficacy of the proposed methods, the results of which were in good agreement with the simulation study findings.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2

REFERENCES

  1. X. Wang, T. M. Fu, L. Zhang, X. Li, X. Liu, T. Amnuaylojaroen, M. T. Latif, Y. Ma, L. Zhang, X. Feng, et al., ‘‘Rapidly changing emissions drove substantial surface and tropospheric ozone increases over Southeast Asia,’’ Geophys. Res. Lett. 49, e2022GL100223 (2022).

  2. T. Amnuaylojaroen, J. Inkom, R. Janta, and V. Surapipith, ‘‘Long rang transport of southeast Asian PM2.5 pollution to northern Thailand during high biomass burning episodes,’’ Sustainability 12, 10049 (2020).

    Article  Google Scholar 

  3. S. Yin, X. Wang, X. Zhang, M. Guo, M. Miura, and Y. Xiao, ‘‘Influence of biomass burning on local air pollution in mainland Southeast Asia from 2001 to 2016,’’ Environ. Pollut. 254, 112949 (2019).

  4. T. Amnuaylojaroen, P. Kaewkanchanawong, and P. Panpeng, ‘‘Distribution and meteorological control of PM2.5 and its effect on visibility in Northen Thailand,’’ Atmosphere 14, 538 (2023).

    Article  Google Scholar 

  5. P. A. Burrough, R. A. McDonnell, and C. D. Lloyd, Principles of Geographical Information Systems (Oxford Univ. Press, Oxford, UK, 2015).

    Google Scholar 

  6. V. Leiva, M. Athayde, C. Azevedo, et al., ‘‘Modeling wind energy flux by a Birnbaum–Saunders distribution with an unknown shift parameter,’’ J. Appl. Stat. 38, 2819–2838 (2011).

    Article  MathSciNet  Google Scholar 

  7. V. Leiva, C. Marchant, F. Ruggeri, and H. Saulo, ‘‘A criterion for environmental assessment using Birnbaum–Saunders attribute control charts,’’ Environmetrics 26, 463–476 (2015).

    Article  MathSciNet  Google Scholar 

  8. V. Leiva, M. Barros, G. A. Paula, and A. Sanhueza, ‘‘Generalized Birnbaum–Saunders distributions applied to air pollutant concentration,’’ Environmetrics 19, 235–249 (2008).

    Article  MathSciNet  Google Scholar 

  9. V. Leiva, M. E. Athayde, C. Azevedo, et al., ‘‘Modelling wind energy flux by a Birnbaum-Saunders distribution with an unknown shift parameter,’’ J. Appl. Stat. 38, 2819–283 (2011).

    Article  MathSciNet  Google Scholar 

  10. C. Marchant, K. Bertin, V. Levia, and H. Saulo, ‘‘Generalized Birnbaum–Saunders kernel density estimators and analysis of financial data,’’ Comput. Stat. Data Anal. 63, 1–15 (2013).

    Article  MathSciNet  Google Scholar 

  11. Y. L. Lio, T. R. Tsai, and S. J. Wu, ‘‘Acceptance sampling plans from truncated life tests based on the Birnbaum–Saunders distribution for percentiles,’’ Commun. Stat. – Simul. Comput. 39, 119–136 (2010).

    Article  MathSciNet  Google Scholar 

  12. Z. W. Birnbaum and S. C. Saunders, ‘‘Estimation for family of life distributions with applications to fatigue,’’ J. Appl. Probab. 6, 328–347 (1969).

    Article  MathSciNet  Google Scholar 

  13. M. Lu and D. S. Chang, ‘‘Bootstrap prediction intervals for the Birnbaum–Saunders distribution,’’ Microelectron. Reliab. 37, 1213–1216 (1997).

    Article  Google Scholar 

  14. H. K. T. Ng, D. Kundu, and N. Balakrishnan, ‘‘Modified moment estimation for the two-parameter Birnbaum–Saunders distribution,’’ Comput. Stat. Data Anal. 43, 283–298 (2003).

    Article  MathSciNet  Google Scholar 

  15. J. Wu and ACM. Wang, ‘‘Improved interval estimation for the two-parameter Birnbaum–Saunders distribution,’’ Comput. Stat. Data Anal. 47, 809–821 (2004).

    Article  MathSciNet  Google Scholar 

  16. B. X. Wang, ‘‘Generalized interval estimation for the Birnbaum–Saunders distribution,’’ Comput. Stat. Data Anal. 56, 4320–4326 (2012).

    Article  MathSciNet  Google Scholar 

  17. Y. Li and A. Xu, ‘‘Fiducial inference for Birnbaum–Saunders distribution,’’ J. Stat. Comput. Simul. 86, 1673–1685 (2016).

    Article  MathSciNet  Google Scholar 

  18. N. Jantakoon and A. Volodin, ‘‘Interval estimation for the shape and scale parameters of the Birnbaum–Saunders distribution,’’ Lobachevskii J. Math. 40, 1164–1177 (2019).

    Article  MathSciNet  Google Scholar 

  19. W. Puggard, S. A. Niwitpong, and S. Niwitpong, ‘‘Confidence intervals for the variance and difference of variances of Birnbaum–Saunders distributions,’’ J. Stat. Comput. Simul. 92, 2829–2845 (2021).

    Article  MathSciNet  Google Scholar 

  20. K. Muralidharan and B. K. Kale, ‘‘Modified gamma distribution with singularity at zero,’’ Commun. Stat. – Simul. Comput. 31, 143–158 (2002).

    Article  MathSciNet  Google Scholar 

  21. S. Niwitpong, S. Koonprasert, and S. A. Niwitpong, ‘‘Confidence interval for the difference between normal population means with known coefficients of variation,’’ Appl. Math. Sci. 6, 47–54 (2012).

    MathSciNet  Google Scholar 

  22. W. Thangjai, S. Niwitpong, and S. A. Niwitpong, ‘‘Confidence intervals for mean and difference between means of normal distributions with unknow coefficients of variation,’’ Mathematics 39 (5), 1–23 (2017).

    Google Scholar 

  23. P. Maneerat, S. A. Niwitpong, and S. Niwitpong, ‘‘Confidence intervals for the mean of delta-lognormal distribution,’’ in Structural Changed and their Econometric Modeling, Studies in Computational Intelligence, Ed. by V. Kreinovich and S. Sriboonchitta (Springer Int., Cham, 2019), pp. 264–274.

    Google Scholar 

  24. P. Maneerat, S. A. Niwitpong, and S. Niwitpong, ‘‘Bayesian confidence intervals for a single mean and the difference between two mean of delta-lognormal distributions,’’ Commun. Stat. – Simul. Comput. 50, 2906–2934 (2019).

    Article  MathSciNet  Google Scholar 

  25. M. La-ongkaew, S. A. Niwitpong, and S. Niwitpong, ‘‘Confidence intervals for the difference between means and ratio of mean of Weibull distribution,’’ in Structural Changes and their Econometric Modeling, Conference Proceedings (Springer, 2018), pp. 364–377.

  26. T. Kaweprasert, S. A. Niwitpong, and S. Niwitpong, ‘‘Bayesian estimation for the mean of delta-gamma distributions with application to rainfall data in Thailand,’’ PeerJ (2022).

  27. T. Ngamkham, A. Volodin, and I. Volodin, ‘‘Confidence intervals for a ratio of binomial proportions based on direct and inverse sampling schemes,’’ Lobachevskii J. Math. 37, 466–496 (2016).

    Article  MathSciNet  Google Scholar 

  28. A. Kokaew, J. Thaithanan, W. Bodhisuwan, and A. Volodin, ‘‘Confidence estimation of a ratio of binomial proportions for dependent populations,’’ Lobachevskii J. Math. 42, 394–403 (2021).

    Article  MathSciNet  Google Scholar 

  29. C. Sungboonchoo, T. Ngamkham, W. Panichkitkosolkul, and A. Volodin, ‘‘Confidence estimation of the cross-product ratio of binomial proportions under different sampling schemes,’’ Lobachevskii J. Math. 42, 435–450 (2021).

    Article  MathSciNet  Google Scholar 

  30. W.-H. Wu and H.-N. Hsieh, ‘‘Generalized confidence interval estimation for the mean of delta-lognormal distribution: An application to New Zealand trawl survey data,’’ J. Appl. Stat. 41, 1471–1485 (2014).

    Article  MathSciNet  Google Scholar 

  31. E. B. Wilson, ‘‘Probable inference the law of succession and statistical inference,’’ J. Am. Stat. Assoc. 22(158), 209–212 (1927).

    Article  Google Scholar 

  32. J. Hannig, ‘‘On generalized fiducial inference,’’ Stat. Sin. 19, 491–544 (2009).

    MathSciNet  Google Scholar 

  33. J. Aitchison, ‘‘On the distribution of a positive random variable having a discrete probability mass at the origin,’’ J. Am. Stat. Assoc. 50, 901–908 (1955).

    MathSciNet  Google Scholar 

  34. S. Weerahandi, ‘‘Generalized confidence intervals,’’ J. Am. Stat. Assoc. 88 (905), 899–905 (1993).

    Article  MathSciNet  Google Scholar 

  35. Z. L. Sun, ‘‘The confidence intervals for the scale parameter of the Birnbaum–Saunders fatigue life distribution,’’ Acta Armament. 30, 1558–1561 (2009).

    Google Scholar 

  36. A. Das Gupta, Asymptotic Theory of Statistics and Probability (Springer, New York, 2008).

    Google Scholar 

  37. M. Engelhardt, L. J. Bain, and F. T. Wright, ‘‘Inferences on the parameters of the Birnbaum-Saunders fatigue life distribution based on maximum likelihood estimation,’’ Technometrics 23, 251–255 (1981).

    Article  MathSciNet  Google Scholar 

  38. B. Efron and R. Tibishirani, An Introduction to the Bootstrap (Chapman and Hall, London, UK, 1993).

    Book  Google Scholar 

  39. A. J. Lemonte, A. B. Simas, and F. Cribari-Neto, ‘‘Bootstrap-based improved estimators for the two-parameter Birnbaum–Saunders distribution,’’ J. Stat. Comput. Simul. 78, 37–49 (2008).

    Article  MathSciNet  Google Scholar 

  40. J. G. Mackinnon and J. A. A. Smith, ‘‘Approximate bias correction in econometrics,’’ J. Econometr. 85, 205–230 (1998).

    Article  MathSciNet  Google Scholar 

  41. J. Hannig, ‘‘Generalized fiducial inference via discretization,’’ Stat. Sin. 23, 489–514 (2013).

    MathSciNet  Google Scholar 

  42. W. R. Gilks and P. Wild, ‘‘Adaptive rejection sampling for Gibbs sampling,’’ J. Appl. Stat. 41, 337–348 (1992).

    Article  Google Scholar 

  43. W. R. Gilks, N. G. Best, and K. K. C. Tan, ‘‘Adaptive rejection metropolis sampling within Gibbs sampling,’’ J. Appl. Stat. 44, 455–472 (1995).

    Article  Google Scholar 

  44. J. Chen, Z. Li, M. Lv, Y. Wang, W. Wang, Y. Zhang, H. Wang, X. Yan, Y. Sun, and M. Cribb, ‘‘Aerosol hygroscopic growth, contributing factors, and impact on haze events in a severely polluted region in northern China,’’ Atmos. Chem. Phys. 19, 1327–1342 (2019).

    Article  Google Scholar 

  45. D. Baumer, B. Vogel, S. Versick, R. Rinke, O. Mohler, and M. Schnaiter, ‘‘Relationship of visibility, aerosol optical thickness and aerosol size distribution in an ageing air mass over South-West Germany,’’ Atmos. Environ. 42 989–998 (2008).

    Article  Google Scholar 

  46. Thai Meteorological Department Automatic Weather System, https://www.tmd.go.th/service/tmdData. Accessed April 20, 2023.

Download references

Funding

This research has received funding support from the National Science, Research and Innovation Fund (NSRF), and King Mongkut’s University of Technology North Bangkok: KMUTNB-FF-67-B-13.

Author information

Authors and Affiliations

  1. Department of Applied Statistics, Faculty of Applied Science, King Mongkut’s University of Technology North Bangkok, Bangkok, Thailand

    Natchaya Ratasukharom, Sa-Aat Niwitpong & Suparat Niwitpong

Authors
  1. Natchaya Ratasukharom
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Sa-Aat Niwitpong
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Suparat Niwitpong
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding authors

Correspondence to Natchaya Ratasukharom, Sa-Aat Niwitpong or Suparat Niwitpong.

Ethics declarations

The authors of this work declare that they have no conflicts of interest.

Additional information

Publisher’s Note.

Pleiades Publishing remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

(Submitted by M. Ünver)

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Ratasukharom, N., Niwitpong, SA. & Niwitpong, S. Confidence Interval Estimation for the Mean of Zero-Inflated Birnbaum–Saunders Distribution. Lobachevskii J Math 44, 5364–5383 (2023). https://doi.org/10.1134/S1995080223120272

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S1995080223120272

Keywords:

Search

Navigation