Hostname: page-component-77c89778f8-vpsfw Total loading time: 0 Render date: 2024-07-17T18:39:58.605Z Has data issue: false hasContentIssue false
  • English
  • Français

III.—On the Moments and Regression Equations of the Fourfold Negative and Fourfold Negative Factorial Binomial Distributions

Published online by Cambridge University Press:  14 February 2012

A. J. B. Wiid
A. J. B. Wiid
Affiliation:
National Physical Laboratory, South African Council for Scientific and Industrial Research, Pretoria, South Africa
Get access Rights & Permissions [Opens in a new window]

Synopsis

The bivariate distribution corresponding to the univariate negative binomial, and the corresponding distribution when sampling is without replacement, are investigated. Formulas are derived for the factorial moment generating functions and for the regression equations, which are linear.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 65 , Issue 1 , 1958 , pp. 29 - 34
Copyright
Copyright © Royal Society of Edinburgh 1958

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 to Literature

Aitken, A. C., and Gonin, H. T., 1935. “On fourfold sampling with and without replacement”, Proc. Roy. Soc. Edin., 55, 114–125.CrossRefGoogle Scholar
Guldberg, S., 1935. “Recurrence formulæ for the semi-invariants of some discontinuous functions of n variables”, Skand. Aktuar. Tidskr., 18, 270–278.Google Scholar
Jordan, C., 1950. Calculus of Finite Differences. p. 48. New York.Google Scholar
Steyn, H. S., 1951. “On discrete multivariate probability functions”, Proc. Acad. Set. Amst., A, 54, 23–30.Google Scholar
Wiid, A. J. B., and Steyn, H. S., 1956. “Uitbreidings van die Binomiale en Faktoriaal-Binomiale Stellings”, Tydskr. Wet. Kuns, 16, 210–217.Google Scholar
Wishart, J., 1949. “Cumulants of multivariate multinomial distributions”, Biometrika, 36, 47–58.CrossRefGoogle Scholar