# chi-square distribution

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## chi-square distribution

(ˈkaɪˌskwɛə)
n
(Statistics) statistics a continuous single-parameter distribution derived as a special case of the gamma distribution and used esp to measure goodness of fit and to test hypotheses and obtain confidence intervals for the variance of a normally distributed variable
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2371 NA The log likelihood test statistics have a chi-square distribution with one degree of freedom.
For some distributions, like t distribution or Chi-square distribution, the t or Chi-square value depends on a single value of degree of freedom only.
t] is large enough, it is possible to use the Central Limit Theorem to approximate the Chi-square distribution to a Gaussian distribution [31], and the following approximation holds
dx,[lambda]] is a left-tail non-central Chi-square distribution with degree of freedom (df) and non-centrality parameter [lambda] = [Nw.
1-[alpha],df] the [alpha]th percentile of the chi-square distribution with df, degrees of freedom, n is the sample size, df = n - m (number of independent random samples) is degrees of freedom defined as the number of values that are free to vary, and Z(1-P)/2 is the pth percentile of the standard normal distribution.
The chi-square distribution test and largest normalized residual tests are used to detect and identify the malicious data [11].
The distinct advantage of the prescribed methods is that it circumvents the uncertainty of sample variance by taking account of the underlying chi-square distribution of sample variance and permits a corrected sample size determination according to the desired assurance probability and expected power considerations.
The calculated statistics is compared with the critical value of the chi-square distribution.
An assumption is also made when using the chi-square distribution as an approximation to the distribution of kh2, is that the frequencies expected under independence should not be "too small".
2] has an asymptotic chi-square distribution with (C-1) (S-1) degrees of freedom.

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