noncentral chi-square distribution

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noncentral chi-square distribution

[‚nän¦sen·trəl ¦kī ‚skwer ‚dis·trə′byü·shən]
(statistics)
The distribution of the sum of squares of independent normal random variables, each with unit variance and nonzero mean; used to determine the power function of the chi-square test.
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Results indicate a noncentral chi-square distribution for rows and columns of the GxE interaction matrix, which was also verified by the Kolmogorov-Smirnov test and Q-Q plot.
KEY WORDS / Genotype and Environment Contribution / GxE Interaction / Noncentral Chi-Square Distribution / Modified F Test /
To verify adhesion of the sum of squares of the simulated data to the noncentral chi-square distribution used of the Kolmogorov-Smirnov test.
The sum of squares due to the effect of genotype divided by their respective degrees of freedom follows a noncentral chi-square distribution with noncentrality parameter [[theta].
has a noncentral chi-square distribution with v degrees of freedom and noncentrality parameter [lambda] = [[SIGMA].
1] has a noncentral chi-square distribution then the distribution of X = [square root of [X.
2] has an independent noncentral chi-square distribution with v degrees of freedom and noncentrality parameter [lambda], then
The statistical power of the chi-square test is evaluated from the noncentral chi-square distribution (Broffitt and Randles, 1977; Guenther, 1977; Weir and Cockerham, 1978).
Tables of the noncentral chi-square distribution yield the power of the test as a function of the noncentrality parameter, the degrees of freedom and the significance level (see Haynam et al.
The distribution function of the test statistic V' is closely approximated by the chi-square distribution with 2TW degrees of freedom in the noise case and by the noncentral chi-square distribution with 2TW degrees of freedom and noncentrality parameter [lamda] = [2E.
Robertson, "Computation of the Noncentral Chi-Square Distribution," Bell System Tech.

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