On Differently Defined Skewness
Pomeranian Academy, Arciszewskiego 22, 76-200 Slupsk, Poland
e-mail: sulewski@zis.pap.edu.pl
Received:
Received: 8 November 2007; accepted: 20 January 2008, published online: 1 April 2008
DOI: 10.12921/cmst.2008.14.01.39-46
OAI: oai:lib.psnc.pl:644
Abstract:
Four definitions of skewness are discussed: classic skewness, two Pearson’s skewnesses and Bowley’s skewness. The ability of these skewnesses to express asymmetry is compared as well as the accuracy of their estimation from normal distribution is assessed.
Key words:
estimator density function, Johnson’s distribution, method of Parzen, skewness
References:
[1] S. Brandt, Data analysis, Warsaw 1998 (in Polish).
[2] H. Cramer, Mathematical method in statistics, Warsaw 1958 (in Polish).
[3] H. A. David, Order statistics, Wiley, New York, 1970.
[4] A. Drapella, Statistical inference on the base skewness and kurtosis, Pomeranian Pedagogical Academy, Slupsk 2004 (in Polish).
[5] N. L. Johnson, System of frequency curves generated by methods of translation, Biometrika 36 (1949).
[6] M. G. Kendal, A. Stuart, The advanced theory of statistics, Distribution theory, 1, London 1958.
[7] J. F. Kenney, E. S. Keeping, Mathematics of statistics, Pt. 1, 3rd ed. Princeton, NJ: Van Nostrand, 101-102 (1962).
[8] E. Parzen, On estimation of a probability density and mode, Ann. Math. Statist, 33, 1065-1076 (1962).
[9] B. W. Silverman, Density estimation, Chapman and Hall, London – New York, 1986.
Four definitions of skewness are discussed: classic skewness, two Pearson’s skewnesses and Bowley’s skewness. The ability of these skewnesses to express asymmetry is compared as well as the accuracy of their estimation from normal distribution is assessed.
Key words:
estimator density function, Johnson’s distribution, method of Parzen, skewness
References:
[1] S. Brandt, Data analysis, Warsaw 1998 (in Polish).
[2] H. Cramer, Mathematical method in statistics, Warsaw 1958 (in Polish).
[3] H. A. David, Order statistics, Wiley, New York, 1970.
[4] A. Drapella, Statistical inference on the base skewness and kurtosis, Pomeranian Pedagogical Academy, Slupsk 2004 (in Polish).
[5] N. L. Johnson, System of frequency curves generated by methods of translation, Biometrika 36 (1949).
[6] M. G. Kendal, A. Stuart, The advanced theory of statistics, Distribution theory, 1, London 1958.
[7] J. F. Kenney, E. S. Keeping, Mathematics of statistics, Pt. 1, 3rd ed. Princeton, NJ: Van Nostrand, 101-102 (1962).
[8] E. Parzen, On estimation of a probability density and mode, Ann. Math. Statist, 33, 1065-1076 (1962).
[9] B. W. Silverman, Density estimation, Chapman and Hall, London – New York, 1986.
