Some Results on the Distribution of Quadratic Forms in Normal Variables | ||
| The Egyptian Statistical Journal | ||
| Article 1, Volume 3, Issue 1, June 1959, Pages 1-16 | ||
| Document Type: Original Article | ||
| DOI: 10.21608/esju.1959.316506 | ||
| Author | ||
| S. H. Abd El-Aty | ||
| Abstract | ||
| 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. | ||
| Keywords | ||
| Quadratic Forms; The Cube; Root Normalization Method; Integrals of a Weighted Sum of Chi; Squares; Finite Series | ||
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