Abstract
This paper derives the sampling distribution of dependent quadratic forms from normal and nonnormal universes. It is shown that when all the population cumulants are finite, under some conditions, the joint distribution of dependent quadratic forms can be expressed as infinite series involving Laquerre polynomials.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Davis, A. W., `Statistical distributions in univariate and mulivariate Edgeworth populations.,’ Biometrika 63 (1976), 661–670.
Jensen, D.R., `The joint distribution of quadratic forms and related distributions,’ Aust. Jour. Statist. 12 (1970a), 13–22.
Jensen, D.R., `The joint distribution of traces of Wishart matrices and their applications,’ Ann. Math. Statist. 41 (1970b), 133–145.
Geary, R.C., `Testing for normality,’ Biometrika 34 (1947), 209–242
Searle, S.R., Linear Models, John Wiley and Sons, New York, 1971
Tan W.Y. and Wong, S.P., `On approximating the central and noncentral multivariate gamma distributions,’ Comm. in Statist B7 (1978), 227–243.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1987 Springer Science+Business Media Dordrecht
About this chapter
Cite this chapter
Tan, W.Y. (1987). Sampling Distributions of Dependent Quadratic Forms from Normal and Nonnormal Universes. In: Gupta, A.K. (eds) Advances in Multivariate Statistical Analysis. Theory and Decision Library, vol 5. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-0653-7_21
Download citation
DOI: https://doi.org/10.1007/978-94-017-0653-7_21
Publisher Name: Springer, Dordrecht
Print ISBN: 978-90-481-8439-2
Online ISBN: 978-94-017-0653-7
eBook Packages: Springer Book Archive