The distributions and probability integrals of some quadratic forms applied in testing the null hypothesis (H₀) in the analysis of variance are reviewed. In the alternative hypothesis (H₁), the distributions of the quadratic forms that almost occur in evaluating the power function are investigated. The author gives in this paper: The cube-root normalization method of the non-central chi-square. Exact formulae for the distribution and probability integrals of a weighted sum of chi-squares with even degrees of freedom are given in finite series. The probability integral for a variable distributed as the ratio of two independent weighted sums of chi-squares, with even degrees of freedom, also given. Special cases and numerical examples are given for illustration and verification.
Abd El-Aty, S. (1959). Some Results on the Distribution of Quadratic Forms in Normal Variables. The Egyptian Statistical Journal, 3(1), 1-16. doi: 10.21608/esju.1959.316506
MLA
S. H. Abd El-Aty. "Some Results on the Distribution of Quadratic Forms in Normal Variables", The Egyptian Statistical Journal, 3, 1, 1959, 1-16. doi: 10.21608/esju.1959.316506
HARVARD
Abd El-Aty, S. (1959). 'Some Results on the Distribution of Quadratic Forms in Normal Variables', The Egyptian Statistical Journal, 3(1), pp. 1-16. doi: 10.21608/esju.1959.316506
VANCOUVER
Abd El-Aty, S. Some Results on the Distribution of Quadratic Forms in Normal Variables. The Egyptian Statistical Journal, 1959; 3(1): 1-16. doi: 10.21608/esju.1959.316506
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