Grade approach to skewness

• Autorzy: Ciok A.
• Języki publikacji: EN

Abstrakty

EN

Two measures of asymmetry, of one random variable with respect to another, are proposed. The first is functional (asymmetry curve) ; the second is numerical (asymmetry index), and is based on the first. Their formal definitions and properties are presented as well as several applicationsto various data. These examples were swpecifically chosen to show the interpretations of the proposed measure and their universality.

PL

Praca przedstawia propozycję dwóch miar asymetrii jednej zmiennej losowej względem drugiej. Pierwsza z nich jest miara funkcyjną (krzywa asymetrii), druga jest numeryczna i bazuje na na pierwszej. W pracy przedstawione zostały zasady zarówno formalne definicje jak i zastosowania do różnych typów danych.

Słowa kluczowe

EN

asymmetry curve; concentration curve; grade transformation

PL

krzywa asymetrii; krzywa koncentracji; przekształcenie gradacyjne

• Wydawca: Instytut Podstaw Informatyki PAN
• Czasopismo: Prace Instytutu Podstaw Informatyki Polskiej Akademii Nauk
• Rocznik: 2002
• Tom: Nr 944
• Strony: 1--16
• Opis fizyczny: Bibliogr. 10 poz.

Twórcy

autor

Ciok A.

• Alicja Ciok Institute of Computer Science, Polish Academy of Sciences 01-237 Warsaw, Ordona 21, Poland,

Bibliografia

• Averous J., Meste M., 1997. Skewness for multivariate distributions: two approaches. The Annals of Statistics, Vol. 25, No. 5, 1984-1997.
• Bickel P. J., Lehmann E. L., 1975. Descriptive statistics for nonparametric models, The Annals of Statistics, Vol. 3, No. 5, 1038-1069.
• Cifarelli D. M., Regazzini E., 1987. On a General Definition of Concentration Function, Sankhya, 307-319.
• Ciok A., 1998. Discretization as a tool in cluster analysis, In: Rizzi A., Vichi M., Bock H.-H (Eds.) Advances in Data Science and Classification, Proceedings of the 6th Conference of the International Federation of Classification Societies (IFCS-98), Rome, July 21-24 1998, Springer, 1998, 349-354.
• Ciok A., 1996. An estimator of Gini Separation Index which is nearly median-unbiased, Com¬putational Statistics & Data Analysis, 21, 533-546.
• Ciok A., Kowalczyk T., Pleszczynska T., 1998. How a New Statistical Infrastructure Induced a New Computing trend in Data Analysis. In: Polkowski L., Skowron A. (Eds.) Rough Sets and Current Trends in Computing, First International Conference, RSCTC’98, Warsaw, Poland June 1998 Proceedings, Lecture Notes in Artificial Intelligence 1424, Springer, 75-82.
• Ciok A., Kowalczyk T., Pleszczynska E., Szczesny W., 1995. Algorithms of grade correspondence- cluster analysis. The Collected Papers of Theoretical and Applied Computer Science, , vol. 7, no 1-4, 5-22.
• Doksum K. A., 1975. Measures of location and asymmetry, Scand. J. Statist. 2, 11-22.
• Kowalczyk T., 1994. A unified Lorenz-type approach to divergence and dependence, Disserta- tiones Mathematicae, CCCXXXV.
• Lehmann E. L., Rojo J., 1992. Invariant directional orderings, The Annals of Statistics, Vol. 20, No. 4, 2100-2110.