Skip to main content
SpringerLink
Log in

Joint Plausibility Regions for Parameters of Skew Normal Family

  • Conference paper
  • First Online:
Book cover Predictive Econometrics and Big Data (TES 2018)

Part of the book series: Studies in Computational Intelligence ((SCI,volume 753))

Included in the following conference series:

  • 2118 Accesses

Abstract

The estimation of parameters is a challenge issue for skew normal family. Based on inferential models, the plausibility regions for two parameters of skew normal family are investigated in two cases, when either the scale parameter \(\sigma \) or the shape parameter \(\delta \) is known. For illustration of our results, simulation studies are proceeded.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 259.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 329.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 329.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Aronld, B.C., Beaver, R.J., Groenevld, R.A., Meeker, W.Q.: The nontruncated marginal of a truncated bivariate normal distribution. Psychometrica 58(3), 471–488 (1993)

    Article  MathSciNet  MATH  Google Scholar 

  2. Azzalini, A.: A class of distributions which includes the normal ones. Scand. J. Stat. 12(2), 171–178 (1985)

    MathSciNet  MATH  Google Scholar 

  3. Azzalini, A.: Further results on a class of distributions which includes the normal ones. Statistica 46(2), 199–208 (1986)

    MathSciNet  MATH  Google Scholar 

  4. Azzalini, A., Capitanio, A.: Statistical applications of the multivariate skew normal distribution. J. R. Stat. Soc. 61(3), 579–602 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  5. Azzalini, A., Capitanio, A.: The Skew-Normal and Related Families, vol. 3. Cambridge University Press, Cambridge (2013)

    Book  MATH  Google Scholar 

  6. Azzalini, A., Dalla Valle, A.: The multivariate skew-normal distribution. Biometrika 83(4), 715–726 (1996)

    Article  MathSciNet  MATH  Google Scholar 

  7. Dey, D. Estimation of the parameters of skew normal distribution by approximating the ratio of the normal density and distribution functions. Ph.D. thesis, University of California Riverside (2010)

    Google Scholar 

  8. Hill, M., Dixon, W.J.: Robustness in real life: a study of clinical laboratory data. Biometrics 38, 377–396 (1982)

    Article  Google Scholar 

  9. Liseo, B., Loperfido, N.: A note on reference priors for the scalar skew-normal distribution. J. Stat. Plan. Inference 136(2), 373–389 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  10. Martin, R., Liu, C.: Inferential models: a framework for prior-free posterior probabilistic inference. J. Am. Stat. Assoc. 108(501), 301–313 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  11. Martin, R.: Random sets and exact confidence regions. Sankhya A 76(2), 288–304 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  12. Martin, R., Liu, C.: Inferential models: reasoning with uncertainty. In: Monographs on statistics and Applied Probability, vol. 145. CRC Press (2015)

    Google Scholar 

  13. Martin, R., Lingham, R.T.: Prior-free probabilistic prediction of future observations. Technometrics 58(2), 225–235 (2016)

    Article  MathSciNet  Google Scholar 

  14. Mameli, V., Musio, M., Sauleau, E., Biggeri, A.: Large sample confidence intervals for the skewness parameter of the skew-normal distribution based on Fisher’s transformation. J. Appl. Stat. 39(8), 1693–1702 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  15. Pewsey, A.: Problems of inference for Azzalini’s skewnormal distribution. J. Appl. Stat. 27(7), 859–870 (2000)

    Article  MATH  Google Scholar 

  16. Sartori, N.: Bias prevention of maximum likelihood estimates for scalar skew-normal and skew-t distributions. J. Stat. Plan. Inference 136(12), 4259–4275 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  17. Wang, T., Li, B., Gupta, A.K.: Distribution of quadratic forms under skew normal settings. J. Multivar. Anal. 100(3), 533–545 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  18. Ye, R., Wang, T., Gupta, A.K.: Distribution of matrix quadratic forms under skew-normal settings. J. Multivar. Anal. 131, 229–239 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  19. Zhu, X., Ma, Z., Wang, T., Teetranont, T.: Plausibility regions on the skewness parameter of skew normal distributions based on inferential models. In: Robustness in Econometrics, pp. 267–286. Springer (2017)

    Google Scholar 

Download references

Acknowledgments

Authors would like to thank Professor Hung T. Nguyen for introducing this interesting and hot research topic to us. Also we would like to thank referee’s valuable comments which led to improvement of this paper.

Author information

Authors and Affiliations

  1. Department of Mathematical Sciences, New Mexico State University, Las Cruces, USA

    Ziwei Ma, Xiaonan Zhu & Tonghui Wang

  2. College of Science, Northwest A&F University, Yangling, China

    Ziwei Ma

  3. Faculty of Economics, Maejo University, Chiang Mai, Thailand

    Kittawit Autchariyapanitkul

Authors
  1. Ziwei Ma
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Xiaonan Zhu
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Tonghui Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Kittawit Autchariyapanitkul
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Tonghui Wang .

Editor information

Editors and Affiliations

  1. Computer Science Department, University of Texas at El Paso, El Paso, Texas, USA

    Vladik Kreinovich

  2. International College, Chiang Mai University, Chiang Mai, Thailand

    Songsak Sriboonchitta

  3. International College, Chiang Mai University, Chiang Mai, Thailand

    Nopasit Chakpitak

Rights and permissions

Reprints and permissions

Copyright information

© 2018 Springer International Publishing AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Ma, Z., Zhu, X., Wang, T., Autchariyapanitkul, K. (2018). Joint Plausibility Regions for Parameters of Skew Normal Family. In: Kreinovich, V., Sriboonchitta, S., Chakpitak, N. (eds) Predictive Econometrics and Big Data. TES 2018. Studies in Computational Intelligence, vol 753. Springer, Cham. https://doi.org/10.1007/978-3-319-70942-0_16

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-70942-0_16

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-70941-3

  • Online ISBN: 978-3-319-70942-0

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics

Search

Navigation