Gradus
VOL 2, NO 2 (2015): AUTUMN (NOVEMBER)
Eloszláscsaládokhoz való illeszkedés vizsgálata
Goodness of fit to family of distribution
Abstract
Eloszláscsaládokhoz való illeszkedés vizsgálata a matematikai statisz- tikának a hipotézisvizsgálathoz tartozó területe. Ennek az összefoglaló cikknek az a célja, hogy áttekintést adjon az ezen a területen elért leg- elso? eredményekro?l. Felidézzük az elso? teszteket, amelyekkel rögzített eloszláshoz való illeszkedést lehet elleno?rizni, valamint, hogy hogyan találták meg ezeknek a tesztstatisztikáknak a határeloszlásait. Majd az elso? összetett illeszkedésvizsgálati módszereket és határeloszlásukat elevenítjük fel. Ezen eljárások két nagy osztályát tárgyaljuk részlete- sen, az egyik a minta eloszlásának és az eloszláscsalád eloszlásainak távolságán alapuló tesztek, a másik a regresszió-, illetve korrelációtesz- tek.
Goodness of fit to family of distribution belongs to hypothesis tests of mathematical statistics. The goal of this paper is to give a summary of the first results of this area. For the overview we recall the first tests which are suitable for goodness of fit to a fixed distribution paying spe- cial attention to the development of the asymptotic theory of goodness of fit tests. The goodness of fit to family of distributions and their asymp- totic theories are considered, focusing on two classes of this procedure: tests of fit based on the empirical distribution function (EDF), and the regression and correlation tests of fit.
Keywords
Kulcsszavak: illeszkedésvizsgálat, határeloszlás-tétel,
Keywords: goddness-of-fit, asymptotic distribution theorem,
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