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Abstract: Robillard's (1972) approach to obtaining an expression for the cumulant generating function of the null distribution of Kendall's S statistic, when one ranking is tied, is extended to the general case where both rankings are tied. An expression is obtained for the cumulant generating function and it is used to provide a direct proof of the asymptotic normality of the standardized score, S= p Var (S), when both rankings are tied. The third cumulant of S is derived and an expression for exact... (Update)
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BibTeX entry: (Update)
@misc{ valz-cumulant,
author = "Paul D. Valz and A. Ian McLeod",
title = "Cumulant Generating Function and Tail Probability Approximations for Kendall's
Score with Tied Rankings",
url = "citeseer.ist.psu.edu/valz94cumulant.html" }
Citations (may not include all citations):131 The Advanced Theory of Statistics (context) - Kendall, Stuart - 1963
73 Rank Correlation Methods (context) - Kendall - 1975
68 Probability Theory (context) - Loeve - 1963
60 Distributions in Statistics: Continuous Univariate Distribut.. (context) - Johnson, Kotz - 1970
16 A class of statistics with asymptotically normal distributio.. (context) - Hoeffding - 1948
5 Time Series Modelling of Water Resources and Environmental S.. (context) - Hipel, McLeod - 1994
3 Systems of Frequency Curves (context) - Elderton, Johnson - 1969
2 Some questions of distribution in the theory of rank correla.. (context) - David, Kendall et al. - 1951
2 Elements of Nonparametric Statistics (context) - Noether - 1967
2 Distributions of Sums of Squares of Rank Differences for Sma.. (context) - Olds - 1938
2 distribution with ties in one ranking (context) - Robillard, Kendall's - 1972
1 Nonparametrics San Francisco: Holden-Day (context) - Lehmann - 1975
1 Significance Testing of the Spearman Rank Correlation Coeffi.. (context) - Statistician, Zar - 1972
1 Edgeworth series for lattice distributions (context) - Kolassa, McCullagh - 1990
1 The upper tail probabilities of Kendall's tau (context) - Best, Gipps - 1974
1 The distribution of Kendall's score S for a pair of tied ran.. (context) - Burr - 1960
1 convergence and exact tables for Spearman's rank correlation.. (context) - Franklin - 1987
1 Journal of the American Statis- 24 tical Association (context) - Klotz - 1966
1 A note on the cumulants of Kendall's S-distribution (context) - Silverstone - 1950
1 Developments in Rank Correlation Procedures (context) - Valz - 1990
1 A simplified derivation of the variance of Kendall's (context) - Valz, McLeod - 1990
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