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| Description
| - The most commonly used nonparametric estimate of a cumulative distribution function F is an empirical distribution function F_n. But F_n is a step function even in case that F is continuous. The present paper aims to provide a smooth estimate of F. Kernel methods seem to be adequate for this purpose. There exist several methods how to choose a bandwidth. We propose a method of bandwidth selection based on a suitable estimate of Mean Integrated Square Error. We also focus on an estimate of a cumulative distribution function in case that random variables X_1,...,X_n are nonnegative. The aforementioned methods are not reliable near the point x=0. In order to avoid this problem we propose a~reflection method. A simulation study is conducted to compare the performance of the different methods of bandwidth choice. Theoretical results are applied to the data concerning the content of toxic material in the fish population in Lake Ontario.
- The most commonly used nonparametric estimate of a cumulative distribution function F is an empirical distribution function F_n. But F_n is a step function even in case that F is continuous. The present paper aims to provide a smooth estimate of F. Kernel methods seem to be adequate for this purpose. There exist several methods how to choose a bandwidth. We propose a method of bandwidth selection based on a suitable estimate of Mean Integrated Square Error. We also focus on an estimate of a cumulative distribution function in case that random variables X_1,...,X_n are nonnegative. The aforementioned methods are not reliable near the point x=0. In order to avoid this problem we propose a~reflection method. A simulation study is conducted to compare the performance of the different methods of bandwidth choice. Theoretical results are applied to the data concerning the content of toxic material in the fish population in Lake Ontario. (en)
- Nejčastěji používaným neparametrickým odhadem distribuční funkce F je empirický odhad F_n. Avšak F_n je schodovitá funkce i v případech, kdy distribuční funkce F je spojitá. Cílem práce je poskytnout hladký odhad F, zde budou použity jádrové odhady. V literatuře existuje několik metod pro volbu optimální šířky okna. Bude zde navržena metoda založená na vhodném odhadu sřední integrální kvadratické chyby (MISE). Zaměříme se také na případ, kdy všechny hodnoty pozorování X_1 ... X_n jsou nezáporné. Zde nastávají problémy při odhadech distribuční funkce F blízko bodu x=0. Abychom se vyhnuli těmto problémům, bude použita tzv. metoda zrcadlení. Cílem simulační studie je porovnat různé metody pro hledání optimální šířky okna. Teoretické výsledky jsou aplikovány na datech toxických látek v rybí populaci v jezeře Ontario. (cs)
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| Title
| - Smooth Estimates of Distribution Functions with Application in Environmental Studies
- Smooth Estimates of Distribution Functions with Application in Environmental Studies (en)
- Hladké odhady distribučních funkcí s aplikací v environmentálních studiích (cs)
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| skos:prefLabel
| - Smooth Estimates of Distribution Functions with Application in Environmental Studies
- Smooth Estimates of Distribution Functions with Application in Environmental Studies (en)
- Hladké odhady distribučních funkcí s aplikací v environmentálních studiích (cs)
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| skos:notation
| - RIV/00216224:14310/07:00022321!RIV08-MSM-14310___
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| http://linked.open.../vavai/riv/strany
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| http://linked.open...avai/riv/aktivita
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| http://linked.open...avai/riv/aktivity
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| http://linked.open...vai/riv/dodaniDat
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| http://linked.open...aciTvurceVysledku
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| http://linked.open.../riv/druhVysledku
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| http://linked.open...iv/duvernostUdaju
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| http://linked.open...titaPredkladatele
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| http://linked.open...dnocenehoVysledku
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| http://linked.open...ai/riv/idVysledku
| - RIV/00216224:14310/07:00022321
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| http://linked.open...riv/jazykVysledku
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| http://linked.open.../riv/klicovaSlova
| - cumulative distribution function; kernel smoothing; reflection method (en)
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| http://linked.open.../riv/klicoveSlovo
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| http://linked.open...ontrolniKodProRIV
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| http://linked.open...v/mistoKonaniAkce
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| http://linked.open...i/riv/mistoVydani
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| http://linked.open...i/riv/nazevZdroje
| - TIES 2007 Book of Abstracts
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| http://linked.open...in/vavai/riv/obor
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| http://linked.open...ichTvurcuVysledku
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| http://linked.open...cetTvurcuVysledku
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| http://linked.open...vavai/riv/projekt
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| http://linked.open...UplatneniVysledku
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| http://linked.open...iv/tvurceVysledku
| - Koláček, Jan
- Horová, Ivanka
- Zelinka, Jiří
- El-Shaarawi, Abdel H.
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| http://linked.open...vavai/riv/typAkce
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| http://linked.open.../riv/zahajeniAkce
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| number of pages
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| http://purl.org/ne...btex#hasPublisher
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| https://schema.org/isbn
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| http://localhost/t...ganizacniJednotka
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| is http://linked.open...avai/riv/vysledek
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