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A probability density function estimation using F-transform
Kybernetika, Tome 46 (2010) no. 3, pp. 447-458 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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.
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.
Classification : 60E99, 62G07, 62G86, 91G80
Keywords: fuzzy transform; probability density function estimation; smoothing filter; financial returns 
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     title = {A probability density function estimation using {F-transform}},
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Holčapek, Michal; Tichý, Tomaš. A probability density function estimation using F-transform. Kybernetika, Tome 46 (2010) no. 3, pp. 447-458. http://geodesic.mathdoc.fr/item/KYB_2010_46_3_a9/

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