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Several representations of the exact cdf of the sum of squares of nindependent gamma-distributed random variables Xi are given, in particular by aseries of gamma distribution functions. Using a characterization of the gammadistribution by Laha, an expansion of the exact distribution of the samplevariance is derived by a Taylor series approach with the former distribution asits leading term. In particular for integer orders alpha some further seriesare provided, including a convex combination of gamma distributions for alpha =1 and nearly of this type for alpha > 1. Furthermore, some representations ofthe distribution of the angle Phi between (X1,...,Xn) and (1,...,1) are givenby orthogonal series. All these series are based on the same sequence of easilycomputed moments of cos(Phi).

Exact distribution of the sample variance from a gamma parent distribution