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  • About
  • The Global ETD Search service is a free service for researchers to find electronic theses and dissertations. This service is provided by the Networked Digital Library of Theses and Dissertations.
    Our metadata is collected from universities around the world. If you manage a university/consortium/country archive and want to be added, details can be found on the NDLTD website.
1

Polinominio skirstinio hipotezių tikrinimas / Testing the hypotheses of polynomial distribution

Vaitiškytė, Asta 03 September 2010 (has links)
Tikrinamos statistinės hipotezės. Darbas susideda iš dviejų dalių: pirmoje dalyje tikrinamos dvi paprastos hipotezės, taikomas statistinis kriterijus, kuris turi tenkinti tokias sąlygas: 1 – pirmos rūšies klaidos tikimybė yra aprėžta, o 2 - antros rūšies klaidos tikimybę mes minimizuojame. Darbe gauta asimptotinė formulė šios antros rūšies klaidos tikimybės elgesio, kai duomenų skaičius n artėja į begalybę. Antroje dalyje tikrinamos trys paprastos hipotezės ir ištirta kaip elgiasi minimali klaidos tikimybė iš visų galimų, kitaip sakant optimalaus minimaksiško kriterijaus klaidos tikimybė, kai duomenų skaičius n neapibrėžtai didėja. Pirmoje dalyje nagrinėjama klaidos tikimybė asimtotiškai mažėja proporcingai Kulbako atstumui, o antroje dalyje atitinkama klaidos tikimybė atitinkamai mažėja proporcingai Čensovo atstumui. Taip pat savo darbo teorinėje dalyje aprašiau šių atstumų savybes. Pabaigoje, kaip pavyzdį paėmus polinominį skirstinį parodėme, kaip yra surandamos šių dviejų rezultatų asimptotinės formulės ir kaip atrodo atitinkamų šių hipotezių tikrinimo asimptotinis elgesys. / Statistical Hypothesis Testing. The work consists of two parts: in the first part two simple hypotheses were tested and a statistical criterion which should meet the following specifications was applied: 1 – the probability of type I error was defined and 2 - the probability of type II error was minimized. The asymptote formula of behaviour of the probability of type II error was obtained in the work when the n number of the data was approaching infinity. In the second part of the work three simple hypotheses were tested. It has been explored how the minimum error probability of all available errors, i.e., the error probability of the optimal minimax criterion, performed when the n number of the data was indefinitely increasing. The error probability analysed in the first part of the work was asymptotically decreasing in proportion to the Kulbak distance while the corresponding error probability analysed in the second part of the work was respectively decreasing in proportion to the Censov distance. Moreover, the properties of the distances mentioned above were described in the theoretical part of the work. The work concludes with choosing a polynomial distribution as an example which has demonstrated how the two asymptote formulas of the two results were obtained and how the asymptotic behaviour of testing of respective hypotheses looked like.
2

Modifikuotas chi kvadrato suderinamumo kriterijus / Modified chi-square goodnees - of - fit test

Bernackaitė, Emilija 25 November 2010 (has links)
Šiame baigiamajame magistro darbe analizuojamos kriterijaus suderinamumo hipotezėms tikrinti savybės. Siekiama jį patikslinti, įvedant kriterijaus statistikos korekciją . Atlikus klasikinio ir modifikuoto kriterijų tikslumo palyginamąją analizę, naudojant modeliuotas reikšmes, padaryta keletas išvadų. Kriterijus, kuris remiasi statistika , šiek tiek patikslina hipotezių tikrinimo rezultatus, tačiau, kai imtis yra pakankamai didelė, kriterijų tikslumas beveik nesiskiria. Be to, kriterijus, kuris remiasi modeliuotomis reikšmėmis taip pat yra pakankamai tikslus. Taigi, naudojantis šiuolaikinėmis pažangiomis technologijomis, ir, modeliuojant pakankamai didelę a.d. imtį, šio kriterijaus galėtų pakakti, kad patikrinti suderinamumo hipotezę. Skaičiavimų palengvinimui sukurtos makroprogramos a.d. momentams skaičiuoti ir a.d. realizacijoms modeliuoti. / The main purpose of this master thesis is to improve the clasical chi square goodness of fit test so that it would depend less on the rule, according to which the data is divided into intervals, and on the hypothetical probabilities. The tasks of the paper are the following: • To examine (according to the literature ([1], [2], [3])) theoretical and applied aspects of constructing chi square test; • To analyse the methods of graphic representation of the empirical characteristics of the data and graphic comparison with their theoretical equivalents. Altogether to look through the ways of dividing the data into intervals (determining their number and length); • To calculate the mean, variance and third central moment of chi square test statistics and to analyse their properties; • To create a macro for counting the previously mentioned three moments using SAS software; • To create a macro for modeling statistics and to construct goodness of fit test according to the modeled values using SAS software; • To construct an aproximate modified chi square goodness of fit test based on a new statistics; • To perform comparison of the clasical and modified goodness of fit tests, having the modeled values; Analysis of graphing the empirical data and comparison with the theoretical equivalents has showed that the distribution (density) is recognised easier when the probabilities of values to be prescribed to certain intervals are equal. This way the execution of computations is easier as... [to full text]

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