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USING THE STABLE DISTRIBUTION TO MONITOR A PROCESS, WHICH DISTRIBUTION IS UNKNOWN

100%
Chmielińska M.
Acta Universitatis Lodziensis. Folia Oeconomica
|
2014
|
vol. 3
|
issue 302
EN
The control chart is a tool of statistical quality control, which is widely used in production. The fulfillment of its basic assumptions, guarantees flawless assessment of correctness of the monitored process. The purpose of this paper is to pay attention to the need to verify the assumptions of the used method and the effects of its unauthorized use, in case of not meeting its assumptions. In this paper a method that uses a family of stable distributions to estimate the unknown probability density of monitored diagnostic variable, is proposed. The estimated density function is the basis for determining the control limits.
2
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k-th record estimator of the scale parameter of the α-stable distribution

80%
Stachura M., Wodecka B.
Statistics in Transition new series
|
2022
|
vol. 23
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issue 4
203-215
EN
Various techniques of scale parameter estimation have been proposed in the case of alpha stable distributions. In the paper, the authors present an estimation technique that involves the k-th record theory. Although this theory is over 40 years old, its implementation in the classical extreme value theory – being the other cornerstone of the presented approach – is quite new, and tempting. Several theoretical properties of the introduced scale parameter estimators are presented. With the use of Monte Carlo methods, a comparative analysis is performed between the approach based on k-th records and approaches based on Hill’s and Pickands’ estimators. Additionally, the paper uses a real-life data set to illustrate how to effectively apply the k-th record estimator of the scale parameter. The research indicates several advantages of the k-th record approach over its other counterparts, especially when dealing with incomplete information about the underlying sample.
3

Propozycja modyfikacji wskaźnika ujawnionej przewagi komparatywnej z wykorzystaniem funkcji wymiernych

51%
Salamaga M.
Zeszyty Naukowe Uniwersytetu Ekonomicznego w Krakowie
|
2013
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issue 923
23-35
PL
Wskaźnik względnej przewagi komparatywnej (RCA) jest wykorzystywany powszechnie do oceny konkurencyjności eksportu towarów i usług oraz przewagi komparatywnej kraju według sektorów produkcji lub grup towarowych. Jego wartości nie są jednak unormowane, co skutkuje określonymi konsekwencjami. Rozkłady wskaźnika RCA są zwykle asymetryczne, niestabilne w czasie, wrażliwe na liczbę sektorów (grup towarowych) i na liczbę krajów w grupie referencyjnej. Utrudnia to porównywalność wartości wskaźnika w ujęciu czasowym i przestrzennym oraz komplikuje wyznaczenie odpowiedniego rozkładu teoretycznego. W artykule zaproponowano pewną metodę transformacji wskaźnika RCA, która umożliwia poprawę niektórych jego własności. Proponowana metoda wykorzystuje transformację przedmiotowego wskaźnika za pomocą rodziny funkcji wymiernych. W pracy analizowano empiryczne rozkłady unormowanego wskaźnika RCA dla towarów grupowanych zgodnie ze standardową międzynarodową klasyfikacją handlu (SITC).
EN
The Revealed Comparative Advantage Index (RCA) is used to estimate the export attractiveness and comparative advantage in the country by industry sectors or commodity groups. This measure has many disadvantages because it ranges from 0 to ∞. Its empirical distribution is strongly asymmetric and is not stable in time. The Revealed Comparative Advantage Index distribution is strongly dependent on the number of reference countries, industries and commodity groups taken under consideration. In consequence, some RCA distribution parameters are not stable. These problematic properties make its outcomes impossible to compare across time and space. The paper proposes transforming the RCA measure into a new index, ranging from –1 to 1, by using a special class of rational functions. The new measure has a symmetric distribution with a stable mean and is independent of the industry sectors or commodity groups. Empirical distributions of the adjusted RCA index are built on the basis of data on Polish export and import commodities by Standard International Trade Classification (SITC).
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