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Notes on line dependent coefficient and multiaverage

100%
Wilkowski A.
Mathematical Economics
|
2011
|
issue 7 (14)
241-251
EN
In this paper we discuss new statistic tools which enable more precise economics data analysis. Firstly, we define line dependent coefficientas a cosine of the angle made of the cross of regression lines. This is the basis thanks to which we can define other nonlinear relation coefficients such as conic dependent coefficient. Just like the classic correlation coefficient, line dependent coefficient is also asymptotically normal. The second part of this article is about multiaverage, a generalization of the classic expected value of the random variable idea. The average may be considered as the root-mean-square average approximation of the random variable with one point. Multiaverage is an approximation of the random variable with more than just one point at the same time (which is important when we talk about random variables, whose distributions are mixtures, or about multimodal densities). While defining multiaverage, we use the standard moments method and some facts from the orthogonal polynomial theory. In this paper we give some numerical examples in which we use the aforementioned tools.
2

ON CHANGING MONEY AND THE BIRTHDAY PARADOX (O rozmienianiu pieniedzy i paradoksie urodzin)

100%
Wilkowski A.
Didactics of Mathematics
|
2010
|
issue 7(10)
127-134
EN
The paper deals with two problems of discrete probability theory that can be included to a curriculum in mathematics or statistics at universities of economics. The first one addresses the question that is interesting for economists: in how many ways one can change a certain amount of money given a fixed set of denominations. One can answer the question using either theoretical or software tools (such as Matlab or Mathematica). The other problem deals with the birthday paradox and its generalization. It is an example when intuition fails.
3
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Internet security

100%
Wilkowski A.
Mathematical Economics
|
2014
|
issue 10(17)
103-114
EN
In this paper we present how to use the ZT-UNITAKOD method for dynamic coding. We also talk about a cryptosystem on which to base an elliptic curve. Finally, we discuss the ways to protect the internet user from phishing.
4
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Remarks on modal value

100%
Wilkowski A.
Mathematical Economics
|
2013
|
issue 9 (16)
105-116
EN
In this paper we talk about modal value, ideal modal and the relationship between stable distributions and the statistical characteristics like modal and ideal modal. The second part of this article is about the properties of normal and skew-normal density. In the third part of the article we present multiaverage. Multiaverage is an approximation of the random variable with more than just one point at the same time (which is important when we talk about random variables, which distributions are mixtures, or about multimodal densities). While defining multiaverage, we use standard moments method and some facts from orthogonal polynomial theory.
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