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EN
Today, the role of digital signatures becoming more and more significant. The signature provides authentication and integrity of a message but quite often other features like additional functionality is required from the signature. Because of that the algorithms used in ordinary signing are not sufficient, they need to be special algorithms with some additional characteristics. Undeniable signatures are a form of digital signature that have two distinctive features: the verification process is interactive (the signatures cannot be verified without signer's cooperation), a disavowal protocol allows to determine whether a given signature is a forgery. These signatures can be used, for example, to protect a software against unauthorized persons. The safety of these signatures is guaranteed by techniques of modern cryptography which is based on advanced mathematical tools and computer technology. The purpose of the article is to present selected schemes (protocols) of undeniable signatures (based on discrete log systems) such as Chaum-van Antwerpen protocol, Chaum-van Antwerpen protocol protecting against disavowal and a convertible undeniable signature protocol. Main definitions and theorems are presented and all described protocols are illustrated with examples.
EN
The study examines the development of the Polish economy as well as the economies of selected European Union countries in the period from 1949 to 2006. Much space is devoted to a comparative analysis of the development economies in the countries concerned. Based on statistical data appropriate synthetic variables were set. Much space is devoted to the theory of the Johansen's method, to present the dependencies occurring in the dynamics of economic development in subsequent subperiods. The method allows for a comparative assessment of the dynamics of time series. The methods are adopted to examine the level of economic development, to determine the period of long-term equilibrium and stability.
EN
Projection Pursuit Regression (PPR) was introduced by J. Friedman and W. Stuetzle in 1981. It is one of the nonparametric regression methods. The benchmark studies show very often the superiority of PPR models over other nonparametric or classical regression models in terms of the test error. PPR produces a "black-box" prediction machine and it suffers from the lack of interpretation. Thus it seems to be an important issue to find the method for evaluating the influence of the predictor variables on the response. We present the procedure that might be used to examine the strength of the influence of every predictor variable on the response variable in Projection Pursuit Regression models.
EN
Since the presence of noise in the data can significantly affect the characteristics of dynamic systems, the aim of the article will be to evaluate effect of reduction of random noise by method of the nearest neighbors on the value of the largest Lyapunov exponent. The test will be conducted on the basis of the economic time series, which consist of closing prices of companies listed on the Warsaw Stock Exchange and the daily exchange rates.
EN
This paper presents the most popular indicators of the tourist function , and supplements them with modern synthetic metrics. The subject of the application of these indicators is to measure of the tourism function in 31 European countries and making their classification according to the values of measurement used. Unusual problem of engaging research area in the country and not in the local formulation allows for a much more clear showing weaknesses of individual metrics that recognize the problem described. A fragmented approach to the tourism function, prompts to use of synthetic measures which prove to be more useful in classifying particular areas.
EN
The Analytic Hierarchy Process (AHP) allows to create a final ranking for a discrete set of decision variants on the basis of an earlier pairwise comparison of all the criteria and all the decision variants within each criterion. The properties of the obtained ranking depend on the quality of pairwise comparisons; this quality can be evaluated on the basis of consistency measured by means of certain measures. The paper discusses a mathematical model which is the foundation of the AHP and a starting point for a new method which allows to significantly reduce – and even eliminate – the inconsistency of pairwise comparisons measured by the consistency index. The proposed method allows to reduce the consistency index well below the threshold of 0.1.
EN
In the paper an idea of cooperation supporting method based on game theory and multicriterial analysis. Because of taking into consideration a cooperation game with empty core an idea of supporting is based on Bondareva's and Shapley's conditions for non-emptyness of the core. There is defined a minimal value which should be added to payoff of great coalition. The minimal value should be profitable. Also an idea of multicriterial support for establish winnings for the players in cooperative game is presented. The problem is considered in case when ad hoc arrangement is irrational in meaning that the allocation of winnings is outside the core of the game. The proposal is based on concept of goal programming and reference point method. The proposed ideas are shown on example of cooperation problem of the three autonomous departments in enterprise.
EN
In the article presents the modification of the binomial model of European option pricing. Adopted namely, that it is appropriate to the weakening of the assumptions about the mechanism of price formation on the underlying instrument. In the proposed option pricing model, mechanism of option pricing formation is described in terms of fuzzy numbers. In the article, also posted selected messages from the scope of fuzzy numbers and options.
EN
In the article, two approaches to IT services risk assessment has been described and compared. The first one is based on fuzzy methods in the opposite to the second one which uses probability. The following hypothesis has been proposed and proved by showing a practical example: fuzzy modeling is more effective than probabilistic in IT services risk assessment.
EN
In this paper multiple criteria decision problem is considered as a noncooperative game. Each criterion is assigned with a player and every feasible (and effective) solution with a pure strategy. Players payoffs result from assessments of solutions in game state where every player chooses the same strategy-solution. In the analysed game status quo situation is a state in which at least one player-criterion chooses different strategy. The problem of payoff definition in such situation is considered in the paper. A proposal is to state pessimistic payoffs in status quo situations as minimal value of payoffs in situations related with considered solutions of multiple criteria problem (exactly multiple criteria choice problem). The proposal is compared with a deterministic model and solution and based on example from Madani and Lund's (2011) work.
EN
Samuelson and Nordhaus (2012: 436) claim that "There is no pattern in the type formulas, the trajectory of the planets or swing of the pendulum, which would be used to predict the duration and timing of business cycles. Rather, they resemble a change in the weather". Nogalski and Klimek showed that in the years 1995-2010, the Polish GDP was forming in a way that made it possible to describe it using a mathematical formula (2015: 302-305). Having done further research, the authors are trying to establish whether Samuelson and Nordhaus are right. In their search for the answer, they conducted research on the "rhythm" of the world economy, European economy and that of several European states, including Poland, basing on the World Bank (WB) data for the years 1983-2013. The paper presents the results of these studies and the results of the analysis of the development of the Polish GDP based on the Central Statistical Office (CSO) data for the years 1995-2014.(original abstract)
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W artykule przedstawiono tablicę trójdzielczą jako test niezależności chi-kwadrat wraz z jego implementacją komputerową w języku VBA. Zbadano też zdolność tablicy trójdzielczej do wykrywania związku między badanymi cechami, określaną jako moc testu. (fragment tekstu)
EN
This paper discusses the theory of contingency tables with particular empha-sis on three-dimension-tables. Their use in statistical surveys is stressed in the article. The three-dimension-table is presented as a chi-square test of indepen-dence and its implementation in VBA (Visual Basic for Applications) language. In this way, users are provided ready-made procedures and functions for carry-ing out surveys in Microsoft Excel. It has been examined also the ability of the three-dimension-table to detect the relationship between the measured traits, referred to as the power of the test. (original abstract)
XX
Artykuł poświęcony jest tablicom dwudzielczym, które są zaliczane do narzędzi statystycznych. Zaproponowano w nim metodę generowania tablic dwudzielczych o rozmiarach iarach (w× k) zwaną metodą „słupkową”. Wykorzystując implementację komputerową testu niezależności dwóch cech, zbadano zdolność tablicy dwudzielczej do wykrywania związku między badanymi cechami oraz obliczono jego siłę wykorzystując współczynnik Cramera. Porównano rzeczywisty rozkład miary rozbieżności dla tablic dwudzielczych z rozkładem teoretycznym, jakim jest rozkład chi-kwadrat o (w −1)(k −1) stopniach swobody. Podjęto próbę odpowiedzi na pytanie, jaki wpływ mają rozmiary tablicy dwudzielczej na zgodność z rozkładem teoretycznym. (abstrakt oryginalny)
EN
This article focuses on bipartite tables, which belong to the statistical tools. The author proposed the method of bipartite tables' generation of(w x k) size named "column " method. By using computer implementation of two independent features' test, the bipartite table capacity to detect relationship between variables was tested and its capacity by use of Cramer coefficient was calculated. The real distribution of discrepancy measure for the bipartite tables was compared with the theoretical distribution, which is chi-square of (w-l)(k-l) degrees of freedom. The author of this article tried to answer on question: what is the influence of bipartite table sizes on its consistency with theoretical distribution. (original abstract)
XX
W części pierwszej, wykorzystując metodę "słupkową", zaproponowano modyfikację testu niezależności dwóch cech polegającą na zastosowaniu statystyki nazwanej "modułową" jako miary rozbieżności pomiędzy rozkładem zaobserwowanym a hipotetycznym. W rozdziale drugim tego opracowania dla proponowanej statystyki modułowej podano wartości krytyczne |X|α według różnej liczebności próby na poziomie istotności α∈{0,01; 0,05; 0,1} (...). W części trzeciej zbadano zdolność tablicy dwudzielczej do wykrywania związku między cechami, określaną jako moc testu oraz porównano uzyskane wyniki z mocą testu niezależności wykorzystującego statystykę X2 z (k-1)(w-1) stopniami swobody. W części ostatniej dokonano sprawdzenia, czy rozkład omawianych w pracy miar rozbieżności tablic dwudzielczych jest zgodny z rozkładem teoretycznym, jakim jest rozkład chi-kwadrat o (w - 1)(k -1) stopniach swobody. (fragment tekstu)
EN
This paper proposes a modification of the classic test of independence chi-square involving the use of modular statistics, as a measure of discrepancy between the observed and hypothetical distribution. Module statistics differs from Pearson chi-square statistics that deviation square of the theoretical and expected empirical probability is replaced by absolute value. For the proposed statistics is given the critical value |X|α by different size samples of significance α∈{0,01; 0,05; 0,1}. The ability of two-part tables was examined to detect a relationship between characteristics, defmed as the power of the test as well as the results were compared with the power of the test of independence, using statistics by X2 z (k -1)(w -1) degrees of freedom. The Author examined whether the distribution of discrepancy measurements of two-part tables is con-sistent with the theoretical distribution of chi-square by X2 z (k-1)(w-1) degrees of freedom. Their usefulness in statistical practice was indicated too. (original abstract)
EN
In the paper three permutation tests of significance of variance components in the linear mixed model are presented. Two of them are permutation versions of classic tests. The third one is based on log-likelihood. In the Monte Carlo simulation studies properties of the permutation tests are compared with properties of the classic likelihood ratio test and Wald test.
EN
Support Vector Machines (SVM) are a state-of-the-art classification method, but they are also suitable, after a special reformulation, to perform a regression task. Similarly to classification, for a nonlinear regression problem, SVMs use the kernel trick and map the input space into a high-dimensional feature space first, and then perform linear regression in the high-dimensional feature space. One can use the model ensemble approach to try to improve the prediction accuracy. The paper presents the comparison of a single SVM, aggregated SVM and other regression models (linear regression, Projection Pursuit Regression, Neural Networks, Regression Trees, Random Forest, Bagging) by the means of a mean squared test set error.
EN
The aim of the paper is twofold - to construct the implied 7-days forward rate and then to utilize its volatility as a indicator both the situation on asset's market and the flexibility of the yield curve construction. The research applies two parametric models: Nelson-Siegel with four and Svensson one with six parameters. The yield curve was created for WIBOR, FRA and swaps rate which let compare the situation on these markets during and after the financial crisis 2007-2009.
XX
Zwrócono uwagę na konieczność podjęcia badań na poziomie mikroekonomicznym w celu rozpoznania uwarunkowań zachowań konsumentów kształtujących popyt na usługi ubezpieczeniowe. Celem opracowania jest wyodrębnienie określonych uwarunkowań demograficznych i socjoekonomicznych popytu na ubezpieczenia życiowe w populacji studentów województwa łódzkiego. Badanie przeprowadzono w styczniu 2003 r. wśród studentów studiów zaocznych i wieczorowych, w czterech niepublicznych uczelniach działających w województwie łódzkim.
EN
The target of the article is to select proper demographic and socio-economic conditions of demand on life insurance in population of students of the Łódzkie voivodship. The survey was conducted in January 2003 among extramural students of non-public universities. In the elaboration for identification of impact of particular variables on demand on life insurance a model of logistic regression was applied. Two-step survey procedure was used. The first step was connected with single parameter, where identified if particular variables: sex, age, civil status, place of living, children, source of maintenance, material status of household can decide about inclination for contracting a life insurance. The second step was connected with variables, which become statistically essential during the first step and was concerned surveying its joint impact. Applied survey method presented that the following variables: age under 29 years, good material situation of household and children decreased probability of contracting a life insurance. Then, the following elements: sex- woman, being in a marriage, living in the city, employment in the public and private sector or running an economic activity will stimulate for demanding on life insurance i.e. increase a chance to contract a life insurance. Received survey results confirm usability of logistic regression model to analyse conditions of demand on life insurance. (original abstract)
XX
W artykule autor koncentruje się na opisie znaczenia i funkcji statystyki w kontekście współczesnych problemów występujących w badaniach i analizie niepewności zjawisk zachodzących w otoczeniu. Rozpatruje on możliwości i ograniczenia dotyczące obiektywnego oraz subiektywnego pomiaru niepewności. Artykuł przedstawia zbiór rozważań (wspartych literaturą) w zakresie skutecznego wykorzystania statystyki w sferze pomiaru niepewności. Jest to także próba wyróżnienia roli statystyki w dzisiejszym świecie z perspektywy rozwoju i postępu cywilizacyjnego. (fragment tekstu)
EN
The article discusses the statistic importance and functions in the context of contemporary questions arising in surveys and analyses of uncertain phenomena occurring in the environment. Possibilities and limits of objective and subjective uncertainty measurements are analysed. The article contains the supported by literature Author's considerations concerning effective using statistics to measure the uncertainty. Simultaneously, this is a trial to distinguish the role of statistics in today's world. (original abstract)
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