Hostname: page-component-cd9895bd7-jn8rn Total loading time: 0 Render date: 2024-12-27T18:19:55.852Z Has data issue: false hasContentIssue false
  • English
  • Français

The distribution of second order moment statistics in a normal system

Published online by Cambridge University Press:  24 October 2008

J. Wishart  and
M. S. Bartlett
J. Wishart
Affiliation:
Clare College
M. S. Bartlett
Affiliation:
Queens' College
Get access Rights & Permissions [Opens in a new window]

Extract

Let x be a normally distributed variable, which may without loss of generality be measured from the mean of the distribution, so that E(x) = 0, E denoting mathematical expectation. Then x satisfies the differential relation

where k2 (otherwise σ2 or (2h2)−1) is the semi-invariant of order 2. Also k1 = 0, and we know that kr = 0 for r > 2.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 28 , Issue 4 , October 1932 , pp. 455 - 459
Copyright
Copyright © Cambridge Philosophical Society 1932

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

(1)Whittaker, E. T. and Watson, G. N., Modern Analysis (2nd Edn. 1915), 239.Google Scholar
(2)Fisher, R. A., Metron, 5, no. 3 (1925), 90–104, 98.Google Scholar
(3)Fisher, R. A., Proc. Lond. Math. Soc. (2), 30 (1929), 199–238.Google Scholar
(4)Helmert, F. R., Astronomische Nachrichten, 88 (1876), 113–132, 122.CrossRefGoogle Scholar
(5)“Student”, Biometrika, 6 (1908), 1–25.CrossRefGoogle Scholar
(6)Romanovsky, V., Metron, 5, no. 4 (1925), 3–46.Google Scholar
(7)Aitken, A. C., Quart. Journ. Math., 2 (1931), 130–135.CrossRefGoogle Scholar
(8)Pearson, K., Jeffery, G. B. and Elderton, E. M., Biometrika, 21 (1929), 164–193.CrossRefGoogle Scholar
(9)Fisher, R. A., Biometrika, 10 (1915), 507–521.Google Scholar
(10)Watson, G. N., Theory of Bessel Functions, 172.Google Scholar
(11)Wishart, J., Biometrika, 20 A (1928), 32–52.CrossRefGoogle Scholar
(12)Wishart, J., Proc. Lond. Math. Soc. (2), 29 (1929), 309–321.CrossRefGoogle Scholar