The Distribution of Quadratic Forms in Non-Normal Variables and an Application to the Variance Ratio
非正态变量二次型的分布及其在方差比中的应用
Summary Good (1968a, b) using non-rigorous arguments, gave an expression for the characteristic function C.F. (x‘A x, t) of a quadratic form in a non-normal random column vector x whose characteristic function is known, where A is positive semi-definite. A general formula for C.F. (x‘A x, t) is proved here, which coincides with Good's expression when x has a real stable characteristic function. In the general formula, A need not be positive semi-definite and this greater…