256
Views
1
CrossRef citations to date
0
Altmetric
Original Articles

Inference for quantile measures of kurtosis, peakedness, and tail weight

Pages 3148-3163 | Received 16 Sep 2014, Accepted 26 May 2015, Published online: 15 Apr 2016

References

  • Balanda, K.P., Macgillivray, H.L. (1988). Kurtosis: a critical review. Am. Stat. 42:111–119.
  • Balanda, K.P., Macgillivray, H.L. (1990). Kurtosis and spread. Can. J. Stat. 18:17–30.
  • Brys, G., Hubert, M., Struyf, A. (2006). Robust measures of tail weight. Comput. Stat. Data Anal. 50:733–759.
  • Croux, C., Haesbroeck, G. (2001). Maxbias curves of robust scale estimates based on subranges. Metrika, 53:101–122.
  • DasGupta, A. (2006). Asymptotic Theory of Statistics and Probability. New York: Springer. DOI: 10.1007/978-0-387-75971-5.
  • David, H.A. (1981). Order Statistics. New York: Wiley.
  • Doksum, K.A. (1975). Measures of location and asymmetry. Scand. J. Stat. 2:11–22.
  • Groeneveld, R.A. (1998). A class of quantile measures for kurtosis. The Am. Stat. 52:325–329.
  • Groeneveld, R.A., Meeden, G. (1984). Measuring skewness and kurtosis. Stat. 33:391–399.
  • Gupta, M.K. (1967). An asymptotically nonparametric test of symmetry. Ann. Math. Stat. 38(3):849–866.
  • Horn, P.S. (1983). A measure for peakedness. Am. Stat. 37:55–56.
  • Johnson, N.L., Kotz, S., Balakrishnan, N. (1994). Continuous Univariate Distributions. Vol. 1. New York: Wiley.
  • Johnson, N.L., Kotz, S., Balakrishnan, N. (1995). Continuous Univariate Distributions. Vol. 2. New York: Wiley.
  • Jones, M.C., Rosco, J.F., Pewsey, A. (2011). Skewness-invariant measures of kurtosis. Am. Stat. 65(2):89–95.
  • Kotz, S., Seier, E. (2009). An analysis of quantile measures of kurtosis. Stat. Pap. 50:553–568.
  • Moors, J.J.A. (1988). A quantile alternative for kurtosis. J. R. Stat. Soc. Ser. D 37:25–32.
  • Morgenthaler, S. Tukey, J.W., (2000). Fitting quantiles: doubling, HR, HQ and HHH distributions. J. Comput. Graphical Stat. 9:180–195.
  • Oja, H. (1981). On location, scale, skewness and kurosis of univariate distributions. Scand. J. Stat. 8:154–168.
  • Pearson, K. (1905). Skew variation, a rejoinder. Biometrika 4:69–212.
  • Pewsey, A. (2005). The large sample distribution of the most fundamental of statistical summaries. J. Stat. Plann. Inference 134:434–444.
  • Rosco, J.F., Jones, M.C., Pewsey, A. (2011). Skew t distributions via the sinh-arcsinh transformation. Test 20(3):630–652.
  • Ruppert, D. (1987). What is Kurtosis? An influence function approach. Am. Stat. 41(1):1–5.
  • Schmid, F., Trede, M. (2003). Simple tests for peakedness, fat tails and leptokkurtosis based on quantiles. Comput. Stat. Data Anal. 43:1–12.
  • Seier, E., Bonett, D. (2003). Two families of kurtosis measures. Metrika 58:59–70.
  • Staudte, R.G. (2013a). Inference for the standardized median. In: Lahiri, S., Schick, A., Sengupta, A., Sriram, N.T., eds. Contemporary Developments in Statistical Theory; a Festscrift in Honour of Professor Hira Lal Koul (pp. 353–363). New York: Springer.
  • Staudte, R.G. (2013b). Distribution-free confidence intervals for the standardized median. STAT 2(1):184–196.
  • Staudte, R.G. (2014). Inference for quantile measures of skewness. Test 23:751–768.
  • Team, R Development Core. (2008). R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing, Vienna, Austria. ISBN 3-900051-07-0.
  • Tukey, J.W. (1965). Which part of the sample contains the information?Proc. Math. Acad. Sci. USA 53:127–134.
  • van Zwet, W.R. (1964). Transformations of random variables. Amsterdam: Math. Zentrum.
  • Wang, J., Serfling, R. (2005). Nonparametric multivariate kurtosis and tailweight measures. Nonparametric Stat. 17:441–456.
  • Withers, C.S., Nadarajah, S. (2011). Bias-reduced estimates for skewness, kurtosis, L-skewness and L-kurtosis. J. Stat. Plann. Inference 141:3839–3861.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.