Abstract
Ordering by spread. In the preceding paper of this series [1] (to which we refer as BL III) we studied the dispersion of a symmetric distribution about its center of symmetry. In the present paper we study a related aspect of dispersion, which does not require the assumption of symmetry but which even in the symmetric case does not coincide with the concept considered in BL III. Roughly speaking, instead of looking at dispersion relative to a fixed point, we now consider the spread of a random variable throughout its distribution. The difference is perhaps best explained in terms of an example.
This paper was prepared with support of U.S. Office of Naval Research Contract No. N00014-69-A-O;W0-1038/NR042-036.
This research was prepared with support of National Science Foundation Grant No. GP-38485.
Chapter PDF
Similar content being viewed by others
References
Bickel, P. J. - Lehman, E. L. (1976). Descriptive statistics for nonparametric models HI. Dispersion. Ann. Statist., 4, 1139–1158.
Brown, G. - Tukey, J. W. (1946). Some distributions of sample means. Ann. Math. Statist. 7, 1–12.
Doksum, K. (1969). Starshaped transformations and the power of rank tests. Ann. Math. Statist., 40, 1167–1176.
Lawrence, M. J. (1975). Inequalities of s-ordered distributions. Ann. Statist., 3, 413–428.
Zwet, van, W. R. (1964). Convex transformations of random variables. Math. Centrum, Amsterdam.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
This chapter is published under an open access license. Please check the 'Copyright Information' section either on this page or in the PDF for details of this license and what re-use is permitted. If your intended use exceeds what is permitted by the license or if you are unable to locate the licence and re-use information, please contact the Rights and Permissions team.
Copyright information
© 2012 Springer Science+Business Media, LLC
About this chapter
Cite this chapter
Bickel, P.J., Lehmann, E.L. (2012). Descriptive Statistics for Nonparametric Models IV. Spread. In: Rojo, J. (eds) Selected Works of E. L. Lehmann. Selected Works in Probability and Statistics. Springer, Boston, MA. https://doi.org/10.1007/978-1-4614-1412-4_45
Download citation
DOI: https://doi.org/10.1007/978-1-4614-1412-4_45
Published:
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4614-1411-7
Online ISBN: 978-1-4614-1412-4
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)