{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,29]],"date-time":"2026-04-29T07:34:02Z","timestamp":1777448042937,"version":"3.51.4"},"reference-count":27,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2020,7,8]],"date-time":"2020-07-08T00:00:00Z","timestamp":1594166400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Algorithms"],"abstract":"<jats:p>We consider a rather general problem of nonparametric estimation of an uncountable set of probability density functions (p.d.f.\u2019s) of the form:     f ( x ;  r )    , where r is a non-random real variable and ranges from     R 1     to     R 2    . We put emphasis on the algorithmic aspects of this problem, since they are crucial for exploratory analysis of big data that are needed for the estimation. A specialized learning algorithm, based on the 2D FFT, is proposed and tested on observations that allow for estimate p.d.f.\u2019s of a jet engine temperatures as a function of its rotation speed. We also derive theoretical results concerning the convergence of the estimation procedure that contains hints on selecting parameters of the estimation algorithm.<\/jats:p>","DOI":"10.3390\/a13070164","type":"journal-article","created":{"date-parts":[[2020,7,8]],"date-time":"2020-07-08T11:47:46Z","timestamp":1594208866000},"page":"164","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["Nonparametric Estimation of Continuously Parametrized Families of Probability Density Functions\u2014Computational Aspects"],"prefix":"10.3390","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-4347-1358","authenticated-orcid":false,"given":"Wojciech","family":"Rafaj\u0142owicz","sequence":"first","affiliation":[{"name":"Department of Computer Engineering, Wroclaw University of Science and Technology, Wyb Wyspianskiego 27, 50 370 Wroclaw, Poland"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2020,7,8]]},"reference":[{"key":"ref_1","first-page":"1559","article-title":"Evaluation of an unknown distribution density from observations","volume":"3","author":"Cencov","year":"1962","journal-title":"Sov. 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