Acta Univ. Agric. Silvic. Mendelianae Brun. 2021, 69(1), 45-49 | DOI: 10.11118/actaun.2021.004

Quadratic Quasinorm and Its Applications in Risk Analysis

Jakub ©ácha1, Veronika Lacinová2, Zdeněk Karpíąek3
1 Department of Statistics and Operation Analysis, Faculty of Business and Economics, Mendel University in Brno, Zemědělská 1, 613 00 Brno, Czech Republic
2 Department of Quantitative Methods, Faculty of Military Leadership, University of Defence, Kounicova 65, 662 10 Brno, Czech Republic
3 Department of Applied Disciplines, STING Academy, Stromovka 1, 637 00 Brno, Czech Republic

This paper deals with the estimation of the probability distribution of the category random variable from its observed values. The gradient estimation presented is based on the f-quasi-norm term. The gradient estimation tends to move away from the empirical distribution towards a uniform distribution. For this reason, it is called the pessimistic estimate. The paper deals with both point and interval estimates. The bootstrap method is used for interval estimates. The theoretical results are illustrated using specific economic data.

Keywords: f-divergence, f-quasi-norm, quadratic quasi-norm, discrete probability distribution, gradient estimation, bootstrap

Received: July 30, 2020; Accepted: December 14, 2020; Published: March 1, 2021  Show citation

ACS AIP APA ASA Harvard Chicago IEEE ISO690 MLA NLM Turabian Vancouver
©ácha, J., Lacinová, V., & Karpíąek, Z. (2021). Quadratic Quasinorm and Its Applications in Risk Analysis. Acta Universitatis Agriculturae et Silviculturae Mendelianae Brunensis, 69(1), 45-49. doi: 10.11118/actaun.2021.004
Share...
Download citation
  • BibTeX (.bib)
  • Bookends (.ris)
  • EasyBib (.ris)
  • EndNote (.enw)
  • EndNote 8 (.xml)
  • ISI WoS (.isi)
  • Medlars (.medlars)
  • Mendeley (.ris)
  • MODS (.xml)
  • Papers (.ris)
  • RefWorks (.txt)
  • RefManager (.ris)
  • RIS (.ris)
  • MS Word (.xml)
  • Zotero (.ris)
    • Open full article

    References

    1. EFRON, B. and TIBSHIRANI, R. J. 1994. An Introduction to the Bootstrap. Boca Raton: Chapman & Hall/CRC.
    2. KARPÍ©EK, Z., JURÁK, P. and ©ÁCHA, J. 2007. Divergences for Discrete Probability Distribution Estimations. In: Summer School DATASTAT '06. Proceedings. Brno: Masaryk University, pp. 287-292.
    3. KARPÍ©EK, Z., NERADOVÁ (LACINOVÁ), V. and ZAMPACHOVÁ, E. 2008. A Contribution to the Estimation of Discrete Probability Distribution. In: MENDEL 2008. 14th International Conference on Soft Computing (pp. 287-292). Brno.
    4. KARPÍ©EK, Z. and NERADOVÁ (LACINOVÁ), V. 2014. Gradient and Line Estimates Employed in Surveyes. In MENDEL 2014. 20th International Conference on Soft Computing. Brno: FSI, VUT Brno, pp. 407-414.
    5. LACINOVÁ, V., KARPÍ©EK, Z. and SADOVSKÝ, Z. 2011. Pessimistic estimates of the probability distribution of a categorical quantity [in Czech: Pesimistické odhady rozdělení pravděpodobnosti kategoriální veličiny]. Informační bulletin České statistické společnosti, 22(2): 138-145.
    6. VAJDA, I. 2004. Theory of Information [in Czech: Teorie informace] Praha: ČVUT.

    This is an open access article distributed under the terms of the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License (CC BY NC ND 4.0), which permits non-comercial use, distribution, and reproduction in any medium, provided the original publication is properly cited. No use, distribution or reproduction is permitted which does not comply with these terms.


    Return to the content