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2019 | 20 | nr 3 | 155--170
Tytuł artykułu

Power Generalization of Chebyshev's Inequality - Multivariate Case

Autorzy
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
In the paper some multivariate power generalizations of Chebyshev's inequality and their improvements will be presented with extension to a random vector with singular covariance matrix. Moreover, for these generalizations, the cases of the multivariate normal and the multivariate t distributions will be considered. Additionally, some financial application will be presented. (original abstract)
Rocznik
Tom
20
Numer
Strony
155--170
Opis fizyczny
Twórcy
  • Cracow University of Economics
Bibliografia
  • BUDNY, K., (2014). A generalization of Chebyshev's inequality for Hilbert-spacevalued random elements. Statistics and Probability Letters, 88, pp. 62-65.
  • BUDNY, K., (2016). An extension of the multivariate Chebyshev's inequality to a random vector with a singular covariance matrix, Communications in Statistics - Theory and Methods, 45 (17), pp. 5220-5223.
  • CHEN, X., (2007). A new generalization of Chebyshev inequality for random vectors. Available at: https://arxiv.org/abs/0707.0805 [Accessed 5 July 2007].
  • CHEN, X., (2011). A new generalization of Chebyshev inequality for random vectors. Available at: https://arxiv.org/abs/0707.0805v2 [Accessed 24 June 2011].
  • JOHNSON, N.L., KOTZ, S., BALAKRISHNAN, N., (1994). Continuous univariate distribution. Vol. 1, 2nd ed. John Wiley & Sons Inc.
  • JOHNSON, N.L., KOTZ, S., BALAKRISHNAN, N., (1995). Continuous univariate distribution, Vol. 2, 2nd ed. John Wiley & Sons Inc.
  • KRITZMAN, M., Li, Y., (2010). Skulls, financial turbulence, and risk management. Financial Analysts Journal, 66 (5), pp. 30-41.
  • KOTZ, S., BALAKRISHNAN, N., JOHNSON, N.L., (2000). Continuous multivariate distribution, Vol. 1: Models and applications, 2nd ed. John Wiley & Sons Inc.
  • LIN, P., (1972). Some characterizations of the multivariate t distribution, Journal of Multivariate Analysis, 2, pp. 339-344.
  • LOPERFIDO, N., (2014). A probability inequality related to Mardia's kurtosis. In: C. Perna, M. Sibillo (eds.). Mathematical and statistical methods of actuarial science and finance, Springer: Springer International Publishing Switzerland 201. pp. 129-132.
  • MARDIA, K.V., (1970). Measures of multivariate skewness and kurtosis with applications, Biometrika, 57 (3), pp. 519-530.
  • MARSHALL, A., OLKIN, I., (1960). Multivariate Chebyshev inequalities, The Annals of Mathematical Statistics, 31, pp. 1001-1014.
  • NAVARRO, J., (2014). Can the bounds in the multivariate Chebyshev inequality be attained? Statistics and Probability Letters, 91, pp. 1-5.
  • NAVARRO, J., (2016). Avery simple proof of the multivariate Chebyshev's inequality. Communications in Statistics - Theory and Methods, 45 (12), pp. 3458-3463.
  • OLKIN, I., PRATT, J.W., (1958). A multivariate Tchebycheff inequality. The Annals of Mathematical Statistics, 29, pp. 226-234.
  • OSIEWALSKI, J., TATAR, J., (1999). Multivariate Chebyshev inequality based on a new definition of moments of a random vector, Przegląd Statystyczny (Stat. Rev.), 2, pp. 257-260.
  • PEARSON, K., (1919). On generalised Tchebycheff theorems in the mathematical theory of statistics, Biometrika,12(3-4), pp. 284-296.
  • STÖCKL, S., HANKE, M., (2014). Financial applications of the Mahalanobis distance, Applied Economics and Finance, 1 (2), pp. 78-84.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.ekon-element-000171599105

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