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1
Content available remote Estimation of return levels with the generalised F distribution
Ryden Jesper
Acta Geophysica
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2026
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vol. 74, no. 3
art. no 140, s. 1--15
EN
Estimation of return levels is crucial for risk assessment in the environmental sciences. Distributional assumptions influence tail behaviour and may affect both point estimates of return levels and their associated confidence intervals. In this paper, we investigate the flexible four-parameter Generalised F (GenF) distribution, which includes several conventional models as special cases. With emphasis on return levels, we compare GenF with the generalised extreme value (GEV) distribution through simulation studies and analyses of river discharge and significant wave height data. Upper-tail asymptotics of the GenF are examined in relation to GEV. Potential numerical challenges in fitting the GenF are discussed. Overall, both models yield similar return-level estimates upto 200 years, while differences mainly concern tail diagnostics and uncertainty quantification; GenF provides a flexible complement to the classical GEV framework.
2
Content available remote Beta distribution and associated Stirling numbers of the second kind
Gismatullin Jakub, Tardivel Patrick
Probability and Mathematical Statistics
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2024
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Vol. 44, Fasc. 1
119--132
EN
This article gives a formula for associated Stirling numbers of the second kind based on the moment of a sum of independent random variables having a beta distribution. From this formula we deduce lower and upper bounds for these numbers, using a probabilistic approach.
3
Content available Analiza efektywności portfela projektów
Cabała P.
Zeszyty Naukowe Politechniki Poznańskiej. Organizacja i Zarządzanie
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2018
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Nr 77
17--29
PL
Celem artykułu jest przedstawienie metodyki badania efektywności portfela projektów. Na początku omówiono znaczenie portfela projektów w kształtowaniu strategii organizacji. Następnie scharakteryzowano proces budowy portfela projektów. Z uwagi na fakt, że liczba potencjalnych portfeli projektów w organizacji może być bardzo duża, konieczna jest algorytmizacja tego procesu. W artykule przyjęto założenie, że podstawą oceny wygenerowanych portfeli są odpowiednie procedury agregacji zysków i ryzyka. Uznano, że w ocenie ryzyka można bezpośrednio wykorzystać parametry rozkładu czasów zakończenia potencjalnych projektów, zgodne z wytycznymi metody PERT i własnościami rozkładu beta. Rozwiązania teoretyczne zilustrowano opisem przypadku, którego celem jest prezentacja możliwości proponowanych rozwiązań metodologicznych.
EN
The aim of the article is to present a method of evaluation of project portfolio effectiveness. At the beginning, the importance of the project portfolio in shaping an organization's strategy is discussed. Then, the process of building the project portfolio is presented. Due to the fact that the number of potential project portfolios in the organization can be very large, it is necessary to algorithmize this process. The article assumes that the assessment of generated portfolios is adequately based on profit and risk aggregation procedures. The article also assumes that in the risk measurement it is possible to use the PERT method guidelines and beta distribution properties. The theoretical solutions are illustrated with a description of a case, which presents the potential of the proposed methodological solutions.
4
Content available Simulation of Diffusion Flows in Two-Phase Multilayered Stochastically Nonhomogeneous Bodies with Non-Uniform Distribution of Inclusions
Chaplya Y., Chernukha O., Davydok A.
TASK Quarterly : scientific bulletin of Academic Computer Centre in Gdansk
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2015
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Vol. 19, No 3
321--351
EN
Admixture diffusion flows are investigated in two-phase randomly nonhomogeneous multilayered strips with non-uniform distributions of inclusions. Cases where the most probable disposition of layered inclusions is located near the body boundary on which the mass source acts in the neighborhood of another boundary and in the middle of the body are considered. The initial-boundary value problem is formulated for the function of random mass flow under conditions of a constant flow on the upper surface and zero concentration of the admixture on the lower surface. Calculation formulae are obtained for the diffusion flow averaged over the ensemble of phase configurations in the particular cases of beta-distribution at zero and nonzero initial concentrations. The dependences of the averaged admixture flows on medium characteristics are established. It is shown that if the admixture diffusion coefficient in inclusions is greater than in the matrix, consolidation of inclusions in the middle of the body leads to an increasing diffusion flow. Simulation of the averaged diffusion flows of the admixture in the multilayered strip is performed for different model variants of a probable disposition of phases in the body and their comparative analysis is carried out.
5
Content available remote The probability measure corresponding to 2-plane trees
Młotkowski W., Penson K. A.
Probability and Mathematical Statistics
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2013
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Vol. 33, Fasc. 2
255--264
EN
We study the probability measure μ0 for which the moment sequence is (3n/n) 1/n+1 . We prove that μ0 is absolutely continuous, find the density function and prove that μ0 is infinitely divisible with respect to the additive free convolution.
6
Content available On the maximum likelihood estimator in the generalized beta regression model
Rydlewski J. P., Mielczarek D.
Opuscula Mathematica
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2012
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Vol. 32, no. 4
761-774
EN
The subject of this article is to present the beta – regression model, where we assume that one parameter in the model is described as a combination of algebraically independent continuous functions. The proposed beta model is useful when the dependent variable is continuous and restricted to the bounded interval. The parameters are obtained by maximum likelihood estimation. We prove that estimators are consistent and asymptotically normal.
7
Content available Using the beta distribution for assessment of availability and reliability of technical transport facilities
Smalko Z., Jaźwiński J.
Journal of KONBiN
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2009
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No. 3-4 (11-12)
87-100
EN
The paper presents the properties of normalized and generalised beta distributions. Possibility of the use of beta distributions to estimate the reliability and safety of technical transport systems is presented. Suggested is an approach to a method of supplementing the inadequate information with data generated in statistical investigation on the grounds of expert estimates employed for estimating the parameters of beta distributions.
PL
W pracy omówiono właściwości znormalizowanego i uogólnionego rozkładu beta. Przedstawiono możliwość stosowania rozkładów beta do szacowania niezawodności i bezpieczeństwa technicznych systemów transportowych. Zaproponowano pewien sposób podejścia do metody uzupełniania niepełnych informacji danymi wygenerowanymi w trakcie badań statystycznych na bazie eksperckich szacunków zastosowanych do szacunkowej oceny parametrów rozkładów beta.
8
Content available remote On the Normalized Cut
Nadarajah S.
Fundamenta Informaticae
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2008
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Vol. 86, nr 1-2
169-173
EN
In the recent paper by Soundararajan and Sarkar (2003), the normalized cut, a graph partitioning measure for perceptual organization, was shown to be a sum of two beta distributed random variables and expressions derived for its mean and mode. Here, it is pointed out that the given expression for the mode is incorrect. The correct expression is derived and the implications of the error discussed.
9
Content available remote The expert method in estimating the parameters of the triangular and beta distributions.
Jaźwiński J., Smalko Z.
Journal of KONBiN
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2006
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No. 1
31--38
EN
Numerous significant events in the course of flying its mission should be included into the only rarely occurring ones. Therefore, the usually insufficient statistical data base should be supplemented using the expert method. In the work the expert method has been applied to determine the parameters of the triangular and beta distribution
10
Content available remote Wykorzystanie metody ekspertowej do oszacowania parametrów rozkładu beta dla oceny nieuszkadzalności i bezpieczeństwa technicznych środków transportowych
Jaźwiński J., Smalko Z.
Problemy Eksploatacji
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2001
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nr 4
169-176
PL
W opracowaniu przedstawiono niektóre właściwości ogólnego rozkładu beta. Wskazano na możliwości zastosowania tego rozkładu w ocenie nieuszkadzalności i bezpieczeństwa technicznych systemów transportowych. Przedstawiono możliwość wykonania analizy statystycznej w warunkach braku danych eksperymentalnych, na podstawie ocen ekspertowych służących do oszacowania parametrów rozkładu beta.
EN
The paper presents the properties of normalized and generalized beta distributions. Possibility of the use of beta distributions to estimate the reliability and safety of technical transport systems is presented. Suggested is an approach to a method of supplementing the inadequate information with data generated in statistical investigation on the grounds of expert estimates employed for estimating the parameters of beta distributions.
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