The exact distribution of indefinite quadratic forms in noncentral normal vectors

DOI10.1007/BF00054797zbMath0857.62051MaRDI QIDQ1817402

Edmund M. Rudiuk, Serge B. Provost

Publication date: 6 March 1997

Published in: Annals of the Institute of Statistical Mathematics (Search for Journal in Brave)

zbMATH Keywords

exact distributionindefinite quadratic formsexact densityWhittaker's functionlinear combinations of independent noncentral chi-square variablessingular normal vectors

Mathematics Subject Classification ID

Multivariate distribution of statistics (62H10) Characterization and structure theory for multivariate probability distributions; copulas (62H05)

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Cites Work

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• On the asymptotic distribution of quadratic forms in uniform order statistics
• Moments of the sampled autocovariances and autocorrelations for a Gaussian white-noise process
• Probability Content of Regions Under Spherical Normal Distributions, I
• Distribution of a Definite Quadratic Form for Non-Central Normal Variates
• Distribution of Quadratic Forms in Normal Random Variables—Evaluation by Numerical Integration
• The Sampling Distribution of the Serial Correlation Coefficient
• Computing the distribution of quadratic forms in normal variables
• Series Representations of Distributions of Quadratic Forms in Normal Variables. I. Central Case
• Distribution of Definite and of Indefinite Quadratic Forms from a Non- Central Normal Distribution
• Numerical inversion of a characteristic function
• Probability Content of Regions Under Spherical Normal Distributions, IV: The Distribution of Homogeneous and Non-Homogeneous Quadratic Functions of Normal Variables
• Inversion Formulae for the Distribution of Ratios
• Distribution of Quadratic Forms and Ratios of Quadratic Forms
• Some Theorems on Quadratic Forms Applied in the Study of Analysis of Variance Problems, I. Effect of Inequality of Variance in the One-Way Classification
• Note on the Distribution of a Definite Quadratic Form