# chi-square distribution

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Related to Chi-squared distribution: T distribution, Beta distribution

## chi-square dis·tri·bu·tion

a variable is said to have a chi-square distribution with K degrees of freedom if it is distributed like the sum of the squares of K independent random variables, each of which has a normal (gaussian) distribution with mean zero and variance one. The chi-square distribution is the basis for many variations of the chi-square(d) test, perhaps the most widely used test for statistical significance in biology and medicine.
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The fault detection rate of using kernel density estimation to calculate the threshold is slightly higher than the chi-squared distribution. Most of the faults can be detected well and they have high FDRS and low FARS.
[[gamma].sub.1] has a chi-squared distribution with 2([N.sub.T] - N - L + 1) degrees of freedom.
anomala, step lengths appeared to have a finite distribution well approximated by a chi-squared distribution (Fig.
Studying various tests for covariance matrices in samples with P=2, 3 and 5 variables in different matrix structures (modification in the variance, in the correlation, and in both), including the LRT, to test the hypothesis that the covariance matrix of a process ([summation]) is equal to a particular matrix ([[summation].sub.0]), PINTO (2009) reported that the LRT approximated by the chi-squared distribution does not control type I errors for samples of size n=10 in bivariate situations and for samples of sizes n=10 and 25 in situations with P=3 and 5 variables.
(3) Furthermore, this result helps us to reconcile the form of the asymptotic approximation proposed in Theorem 1 with the weighted chi-squared distribution that arises in some special cases as in Example 2 above.
=4 k RMAPE1 RMAPE3 RMAPE5 RMAPE7 RMAPE9 U 3 RMAPE1 -- 0.000 0.000 0.000 0.000 RMAPE3 -- -- 0.821 0.117 0.003 RMAPE5 -- -- -- 0.008 0.005 RMAPE7 -- -- -- -- 0.041 5 RMAPE1 -- 0.000 0.000 0.000 0.000 RMAPE3 -- -- 0.082 0.016 0.000 RMAPE5 -- -- -- 0.255 0.001 RMAPE7 -- -- -- -- 0.051 7 RMAPE1 -- 0.000 0.000 0.000 0.000 RMAPE3 -- -- 0.066 0.067 0.003 RMAPE5 -- -- -- 0.803 0.141 RMAPE7 -- -- -- -- 0.038 9 RMAPE1 -- 0.000 0.000 0.000 0.000 RMAPE3 -- -- 0.022 0.012 0.000 RMAPE5 -- -- -- 0.579 0.084 RMAPE7 -- -- -- -- 0.048 Table 12 P-values from Pair-wise T-tests on Means of MAD's from MA(1), MA(3), MA(5), MA(7), MA (9) for the Chi-squared Distribution with c.v.
From the obtained empirical distributions for the ML QTL positions, [LRT.sub.p] had a chi-squared distribution with 2 degrees of freedom corrected (Bonferroni correction) for 4.5 to 7 independent traits when testing the seven traits.
A further indication of the importance of using a variable counting time scheme can be seen from the analysis of the cumulative chi-squared distribution for the refinement of the structure of famotidine (Figure 4).
This deflation factor is then applied to the observed G statistic, which is then compared with the chi-squared distribution to calculate the final P value.
Denoting the ratio of the restricted value to the unrestricted value as [lambda], the test relies on the fact that -2ln[lambda] follows a chi-squared distribution.
where [[chi square].sub.1] is a chi-squared distribution with 1 degree of freedom.

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