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1

A method of assigning a global preference index

Maciejewski W., Kordecki W.

Operations Research and Decisions

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2017

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Vol. 27, No. 2

59--75

EN

The issue of decision-making has been examined based on the preferences of the entire population, when the preferences of a few subpopulations varying significantly in size are known. The purpose of assigning global preferences according to the coefficients proposed here was to avoid marginalising the preferences of the smaller subpopulations. The preference coefficients for the population have been assigned using a weighted arithmetic mean, where the weights are the square roots of the sizes of the subpopulations. This is similar to the voting system known as the “Jagiellonian compromise”. The statistical properties of these constants were presented in the context of decision making. These results have been illustrated by way of an example where the subpopulations exhibit significant differences, viz. students’ choice of an economics university in Lower Silesia, Poland.

2

Ruin probability of a discrete-time risk process with proportional reinsurance and investment for exponential and Pareto distributions

Jasiulewicz H., Kordecki W.

Operations Research and Decisions

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2015

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Vol. 25, No. 3

17--38

EN

The paper focuses on a quantitative analysis of the probability of ruin in a finite time for a discrete risk process with proportional reinsurance and investment of the financial surplus. It is assumed that the total loss on a unit interval has either a light-tailed distribution – exponential distribution or a heavytailed distribution – Pareto distribution. The ruin probabilities for the finite-horizons 5 and 10 were determined from recurrence equations. Moreover, the upper bound of the ruin probability is given for the exponential distribution based on the Lundberg adjustment coefficient. This adjustment coefficient does not exist for the Pareto distribution, hence an asymptotic approximation is given for the ruin probability when the initial capital tends to infinity. The numerical results obtained are illustrated by tables and figures.

3

q-analogs of order statistics

Kordecki W., Łyczkowska-Hanćkowiak A.

Probability and Mathematical Statistics

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2010

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Vol. 30, Fasc. 2

207--214

EN

We introduce the notion of the q-analog of the k-th order statistics. We give a distribution and asymptotic distributions of q-analogs of the k-th order statistics and the intermediate order statistics with r → ∞ and r − k → ∞ in the projective geometry PG (r − 1; q).

4

Parametryzacja zmian w czasie typowych charakterystyk dzieci w okresie rozwoju

Kordecki W., Pilecki W.

Prace Naukowe Politechniki Warszawskiej. Elektronika

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2007

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z. 161

43-48

EN

In the paper the metod enabling comparison of the measuring results with the typical characteristic of newborn and young children is presented. An example of the brainstem auditory evoked potentials interpeak I-V latency is given.

5

Convolutions of erlang and of Pascal distributions with applications to reliability

Jasiulewicz H., Kordecki W.

Demonstratio Mathematica

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2003

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Vol. 36, nr 1

231--238

EN

The main aim of the paper is to give a generalization of the results given by Sen and Balakrishnan in [7]. The results obtained are used to calculate the reliability of some class of systems.

6

Oszacowania niezawodności systemów

Kordecki W.

Matematyka Stosowana : matematyka dla społeczeństwa

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2002

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Nr 3

71-90

7

Limit Distributions of the Capacity of Large Regular Channel Graphs

Kordecki W.

International Journal of Applied Mathematics and Computer Science

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1999

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Vol. 9, no 2

421-434

EN

The paper is devoted to the investigation of reliability of large channel graphs having links with low reliabilities. Under some regularity assumptions regarding such graphs, we derive bounds and limit distributions of their capacities. The main goal of the paper is to prove a Poisson convergence of the capacity.