On Goodness-of-Fit Tests for Tree Diameter Probality Models

Abstract

Šiame straipsnyje tiriame skersmens tankiu iverciu tinkamumo testus. Lorenco kreiv placiai naudojama biologiniuose tyrimuose augalu nevienodo augimo ir derlingumui ivertinti. Darbe greta žinomu Kolmogorovo-Smirnovo, Kramerio von Mizes, Andersono-Darlingo, hi kvadratu testu analizuojamas naujas testas, kuris pagristas Lorenco kreiv s savyb mis. Šis testas leidžia analizuoti imtis, kuriose steb jimai X1, X2, …, Xn yra nepriklausomi, taciau nebutinai turi vienodus skirstinius. Suformuluotas testas gali buti naudojamas difuziniu procesu tankiu analizei. Naudodami ši testa, galime ivertinti ar du medynai yra vienodai pasiskirste. Medyno medžiu skersmens skirstiniui testuoti naudojami duomenys surinkti pušies medynu pastoviuose bareliuose Dubravoje. Matematiniai skaiciavimai atlikti naudojant simboline algebros sistema MAPLE 11

In the present paper we focus on the problem of the goodness-of-fit tests for diameter density estimates. Lorenz curves are used to describe inequality in plant size and fecundity. Here we propose an easily computed goodness-of-fit test based on the sample generalized Lorenz curve, for a sequence X1, X2, …, Xn of independent random variables with univariate probability cumulative distribution function Fi(x). The proposed test is distribution free. This test can be used to ascertain if the diameter distributions of several forests are similar. We simulate p-value for all the studied tests. To test the diameter distribution as an illustrative experience a real data set is used from the repeated measurements on permanent sample plots of pine stands in Dubrava district. The results are implemented in the symbolic computational language MAPLE. Probability, test, diameter, Kolmogorov, Lorenz