Skip to main content
SpringerLink
Log in

Statistical Estimation with a Known Quantile and Its Application in a Modified ABC-XYZ Analysis

  • Conference paper
  • First Online:
Statistical Modeling and Simulation for Experimental Design and Machine Learning Applications (SimStat 2019)

Part of the book series: Contributions to Statistics ((CONTRIB.STAT.))

Included in the following conference series:

  • 106 Accesses

Abstract

The manuscript suggests an estimator of a functional of a cumulative distribution function (c.d.f.) modified with a known quantile. The modified estimator is unbiased, asymptotically normally distributed with a smaller asymptotic variance than the estimator obtained by plugging in an empirical c.d.f. instead of an unknown c.d.f. This new estimator is applied to modify ABC-XYZ analysis of a trade company’s assortment. As a result, a new merchandise grouping is suggested with a more stable inventory management.

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 149.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD 199.99
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. Botero, B., Francés, F.: Estimation of high return period flood quantiles using additional non-systematic information with upper bounded statistical models. Hydrol. Earth Syst. Sci. 14(12), 2617–2628 (2010)

    Article  Google Scholar 

  2. Chen, J., Sitter, R.:A pseudo empirical likelihood approach to the effective use of auxiliary information in complex surveys. Stat. Sin. 9(2), 385–406 (1999)

    Google Scholar 

  3. Dickie, H.F.: ABC inventory analysis shoots for dollars not pennies. Factory Manag. Maint. 109(7), 92–94 (1951)

    Google Scholar 

  4. Dmitriev, Y., Tarassenko, P., Ustinov, Y.: On estimation of linear functional by utilizing a prior guess. In: International Conference on Information Technologies and Mathematical Modelling, pp. 82–90. Springer, Berlin (2014)

    Google Scholar 

  5. Dmitriev, Y.G., Koshkin, G.M.: Nonparametric estimators of probability characteristics using unbiased prior conditions. Stat. Pap. 59(4), 1559–1575 (2018)

    Article  MathSciNet  MATH  Google Scholar 

  6. Hinkley, D.: On estimating a symmetric distribution. Biometrika 63(3), 680–681 (1976)

    Article  MathSciNet  MATH  Google Scholar 

  7. Jhajj, H., Sharma, M., Grover, L.: A family of estimators of population mean using information on auxiliary attribute. Pakistanian J. Stat. (All Series) 22(1), 43 (2006)

    Google Scholar 

  8. Kabanova, S., Zenkova, Z.N., Danchenko, M.A.: Regional risks of artificial forestation in the steppe zone of Kazakhstan (case study of the green belt of astana). In: IOP Conference Series: Earth and Environmental Science, vol. 211, pp. 12–55. IOP Publishing (2018)

    Google Scholar 

  9. Naik, V., Gupta, P.: A note on estimation of mean with known population proportion of an auxiliary character. J. Ind. Soc. Agric. Stat 48(2), 151–158 (1996)

    Google Scholar 

  10. Owen, A.B.: Empirical Likelihood. Chapman and Hall/CRC (2001)

    Google Scholar 

  11. Shabbir, J., Gupta, S.: Estimation of the finite population mean in two phase sampling when auxiliary variables are attributes. Hacettepe J. Math. Stat. 39(1), 121–129 (2010)

    MathSciNet  MATH  Google Scholar 

  12. Singh, R., Chauhan, P., Sawan, N., Smarandache, F.: Ratio estimators in simple random sampling using information on auxiliary attribute. Auxiliary Inform. A priori Values Constr. Improved Estimators 1, 7 (2007)

    Google Scholar 

  13. Tarima, S.: Statistical estimation in the presence of possibly incorrect model assumptions. J. Stat. Theory Pract. 11(3), 449–467 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  14. Tarima, S., Dmitriev, Y.: Statistical estimation with possibly incorrect model assumptions. Bull. Tomsk State Univ. Control Comput. Inform. 8, 78–99 (2009)

    Google Scholar 

  15. Tarima, S., Pavlov, D.: Using auxiliary information in statistical function estimation. ESAIM: Probab. Stat. 10, 11–23 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  16. Tarima, S.S., Vexler, A., Singh, S.: Robust mean estimation under a possibly incorrect log-normality assumption. Commun. Stat.-Simul. Comput. 42(2), 316–326 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  17. Zaman, T.: Modified ratio estimators using coefficient of skewness of auxiliary attribute. Int. J. Mod. Math. Sci. 16(2), 87–95 (2018)

    Google Scholar 

  18. Zenkova, Z.: Censored data treatment using additional information in intelligent medical systems. In: AIP Conference Proceedings, vol. 1688. AIP Publishing (2015)

    Google Scholar 

  19. Zenkova, Z., Kabanova, T.: The ABC-XYZ analysis modified for data with outliers. In: 2018 4th International Conference on Logistics Operations Management (GOL), pp. 1–6. IEEE (2018)

    Google Scholar 

  20. Zenkova, Z., Lanshakova, L.: Kolmogorov goodness-of-fit test for s -symmetric distributions in climate and weather modeling. IOP Conf. Series: Earth Environ. Sci. 48, 012006 (2016)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Applied Mathematics and Computer Science, Tomsk State University, Tomsk, Russia

    Zhanna Zenkova, Wilson Musoni & Yuriy Dmitriev

  2. Institute for Health and Equity, Medical College of Wisconsin, Milwaukee, WI, USA

    Sergey Tarima

Authors
  1. Zhanna Zenkova
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Sergey Tarima
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Wilson Musoni
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Yuriy Dmitriev
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Zhanna Zenkova .

Editor information

Editors and Affiliations

  1. Department of Statistics, University of Klagenfurt, Klagenfurt, Austria

    Jürgen Pilz

  2. Department of Stochastic Simulation, St. Petersburg State University, St. Petersburg, Russia

    Viatcheslav B. Melas

  3. Department of Artificial Intelligence and Human Interfaces, Paris Lodron University Salzburg, Salzburg, Austria

    Arne Bathke

Rights and permissions

Reprints and permissions

Copyright information

© 2023 The Author(s), under exclusive license to Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Zenkova, Z., Tarima, S., Musoni, W., Dmitriev, Y. (2023). Statistical Estimation with a Known Quantile and Its Application in a Modified ABC-XYZ Analysis. In: Pilz, J., Melas, V.B., Bathke, A. (eds) Statistical Modeling and Simulation for Experimental Design and Machine Learning Applications. SimStat 2019. Contributions to Statistics. Springer, Cham. https://doi.org/10.1007/978-3-031-40055-1_10

Download citation

Publish with us

Policies and ethics

Search

Navigation