Gaussian approximation to a bivariate quadratic form distribution
- 1 October 1979
- journal article
- research article
- Published by Taylor & Francis in Journal of Statistical Computation and Simulation
- Vol. 9 (4) , 253-260
- https://doi.org/10.1080/00949657908810329
Abstract
Consider a joint variable (U 1,U 2) where U 1 and U 2 are represented as follows where Q 1,Q 2 are given positive semi definite matrices represents a chi-square random variable with νdegrees of freedom, η is a p-variate normal random vector with mean equals zero and dispersion matrix depending on a single parameter being independent. Ratio U 1/U 2 occurs in testing the equality of variances of two linear models with the same regression parameters. Here, a bivariate Gaussian approxi-mation to the distribution of is investigated through finding the distri-bution of U 1/U 2. Some other applications are also cited.Keywords
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