Wyniki wyszukiwania - Biblioteka Nauki

1

The Notion of the Diameter of Mereological Ball in Tarski's Geometry of Solids

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Sitek G.

Logic and Logical Philosophy

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2017

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tom 26

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nr 4

531–562

EN

In the paper "Full development of Tarski's geometry of solids" Gruszczyński and Pietruszczak have obtained the full development of Tarski’s geometry of solids that was sketched in [14, 15]. In this paper 1 we introduce in Tarski’s theory the notion of congruence of mereological balls and then the notion of diameter of mereological ball. We prove many facts about these new concepts, e.g., we give a characterization of mereological balls in terms of its center and diameter and we prove that the set of all diameters together with the relation of inequality of diameters is the dense linearly ordered set without the least and the greatest element.

2

Estimation of regression parameters of two dimensional probability distribution mixtures

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Sitek G.

Studia Ekonomiczne

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2016

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tom 304

30-46

EN

We use two methods of estimation parameters in a mixture regression: maximum likelihood (MLE) and the least squares method for an implicit interdependence. The most popular method for maximum likelihood esti-mation of the parameter vector is the EM algorithm. The least squares method for an implicit interdependence is based solving systems of nonlinear equations. Most frequently used method in the estimation of parameters mixtures regression is the method of maximum likelihood. The article presents the possibility of using a different the least squares method for an implicit interdependence and compare it with the maximum likelihood method. We compare accuracy of two methods of estimation by simulation using bias: root mean square error and bootstrapping standard errors of estimation.

PL

Do estymacji parametrów mieszanek regresji stosujemy dwie metody: metodę największej wiarygodności oraz metodę najmniejszych kwadratów dla zależności niejawnych. Najbardziej popularną metodą polegającą na maksymalizacji funkcji wiarygodności jest algorytm EM. Metoda najmniejszych kwadratów dla zależności niejawnych polega na rozwiązaniu układu równań nieliniowych. Najczęściej stosowaną metodą estymacji parametrów mieszanek regresji jest metoda największej wiarygodności. W artykule pokazano możliwość zastosowania innej metody najmniejszych kwadratów dla zależności niejawnych. Obie metody porównujemy symulacyjnie, używając obciążenia estymatora, pierwiastka błędu średniokwadratowego estymatora oraz bootstrapowe błędy standardowe.

3

Sum of gamma and normal distribution

100%

Sitek G.

Zeszyty Naukowe. Organizacja i Zarządzanie / Politechnika Śląska

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2020

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tom z. 143

275--284

EN

Purpose: The article shows how to model audit errors using mixtures of probability distribution. Design/methodology/approach: In financial accounting, data about the economic activities of a given firm is collected and then summarized and reported in the form of financial statements. Auditing, on the other hand, is the independent verification of the fairness of these financial statements. An item in an audit sample produces two pieces of information: the book (recorded) amount and the audited (correct) amount. The difference between the two is called the error amount. The book amounts are treated as values of a random variable whose distribution is a mixture of the distributions of the correct amount and the true amount contaminated by error. The mixing coefficient is equal to the proportion of the items with non-zero errors amounts. Findings: The sum of normal and gamma distribution can be useful for modeling audit errors. Originality/value: In this paper, the method of moments is proposed to estimate mixtures of probability distribution, and we derive a formulation of the probability distribution of the sum of a normally distributed random variable and one with gamma distribution. This research could be useful in financial auditing.

4

Modeling income on the basis of distribution mixture

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Sitek G.

Mathematical Economics

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2014

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nr 10(17)

79-90

EN

Finite mixtures of probability distributions may be successfully used in the modeling of probability distributions of incomes. These distributions are typically heavy tailed and positively skewed. This article deals with the problem of determining the number of components in mixture modeling. This paper considers the likelihood of ratio-based testing of the null hypothesis of homogeneity in mixture models. The number of components is an important parameter in the applications of finite mixture models.