A probability density function estimation using F-transform

Michal Holčapek; Tomaš Tichý

Kybernetika (2010)

  • Volume: 46, Issue: 3, page 447-458
  • ISSN: 0023-5954

Abstract

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The aim of this paper is to propose a new approach to probability density function (PDF) estimation which is based on the fuzzy transform (F-transform) introduced by Perfilieva in [10]. Firstly, a smoothing filter based on the combination of the discrete direct and continuous inverse F-transform is introduced and some of the basic properties are investigated. Next, an alternative approach to PDF estimation based on the proposed smoothing filter is established and compared with the most used method of Parzen windows. Such an approach can be of a great value mainly when dealing with financial data, i. e. large samples of observations.

How to cite

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Holčapek, Michal, and Tichý, Tomaš. "A probability density function estimation using F-transform." Kybernetika 46.3 (2010): 447-458. <http://eudml.org/doc/196338>.

@article{Holčapek2010,
abstract = {The aim of this paper is to propose a new approach to probability density function (PDF) estimation which is based on the fuzzy transform (F-transform) introduced by Perfilieva in [10]. Firstly, a smoothing filter based on the combination of the discrete direct and continuous inverse F-transform is introduced and some of the basic properties are investigated. Next, an alternative approach to PDF estimation based on the proposed smoothing filter is established and compared with the most used method of Parzen windows. Such an approach can be of a great value mainly when dealing with financial data, i. e. large samples of observations.},
author = {Holčapek, Michal, Tichý, Tomaš},
journal = {Kybernetika},
keywords = {fuzzy transform; probability density function estimation; smoothing filter; financial returns; fuzzy transform; probability density function estimation; smoothing filter; financial returns},
language = {eng},
number = {3},
pages = {447-458},
publisher = {Institute of Information Theory and Automation AS CR},
title = {A probability density function estimation using F-transform},
url = {http://eudml.org/doc/196338},
volume = {46},
year = {2010},
}

TY - JOUR
AU - Holčapek, Michal
AU - Tichý, Tomaš
TI - A probability density function estimation using F-transform
JO - Kybernetika
PY - 2010
PB - Institute of Information Theory and Automation AS CR
VL - 46
IS - 3
SP - 447
EP - 458
AB - The aim of this paper is to propose a new approach to probability density function (PDF) estimation which is based on the fuzzy transform (F-transform) introduced by Perfilieva in [10]. Firstly, a smoothing filter based on the combination of the discrete direct and continuous inverse F-transform is introduced and some of the basic properties are investigated. Next, an alternative approach to PDF estimation based on the proposed smoothing filter is established and compared with the most used method of Parzen windows. Such an approach can be of a great value mainly when dealing with financial data, i. e. large samples of observations.
LA - eng
KW - fuzzy transform; probability density function estimation; smoothing filter; financial returns; fuzzy transform; probability density function estimation; smoothing filter; financial returns
UR - http://eudml.org/doc/196338
ER -

References

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  9. Parzen, E., 10.1214/aoms/1177704472, Ann. Math. Statist. 33 (1962), 1065–1076. MR0143282DOI10.1214/aoms/1177704472
  10. Perfilieva, I., Fuzzy transforms: Theory and applications, Fuzzy Sets and Systems 157 (2006), 8, 993–1023. Zbl1092.41022MR2218243
  11. Perfilieva, I., Valášek, R., Fuzzy transforms in removing noise, In: Innovation in Hybrid Intelligent Systems. Springer-Verlag, Berlin – Heidelberg 2005. 
  12. Silverman, B. W., Density Estimation for Statistics and Data Analysis, Chapman & Hall/CRC, London 1986. Zbl0617.62042MR0848134
  13. Simonoff, J. S., Smoothing Methods in Statistics, Springer-Verlag, New York 1996. Zbl0859.62035MR1391963
  14. Stefanini, L., Fuzzy transforms and smooth function, In: Proc. IFSA/EUSFLAT 2009, Lisabon 2009. 

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