Chi-Squared Probability Distribution Family
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A Chi-Squared Probability Distribution Family is a Gamma distribution family (of Chi-squared functions) that is based on a sum of squares of [math]\displaystyle{ k }[/math] independent standard normal random variables.
- Context:
- It can be instantiated in a Chi-Squared Function (to produce a Chi-squared score).
- Example(s):
- Counter-Example(s):
- See: Chi Distribution, Confidence Interval, Friedman Test, Standard Normal, Hypothesis Testing.
References
2016
- (Wikipedia, 2016) ⇒ https://en.wikipedia.org/wiki/chi-squared_distribution Retrieved:2016-5-17.
- In probability theory and statistics, the chi-squared distribution (also chi-square or χ²-distribution) with k degrees of freedom is the distribution of a sum of the squares of k independent standard normal random variables. It is a special case of the gamma distribution and is one of the most widely used probability distributions in inferential statistics, e.g., in hypothesis testing or in construction of confidence intervals.[1][2][3][4] When it is being distinguished from the more general noncentral chi-squared distribution, this distribution is sometimes called the central chi-squared distribution.
The chi-squared distribution is used in the common chi-squared tests for goodness of fit of an observed distribution to a theoretical one, the independence of two criteria of classification of qualitative data, and in confidence interval estimation for a population standard deviation of a normal distribution from a sample standard deviation. Many other statistical tests also use this distribution, like Friedman's analysis of variance by ranks.
- In probability theory and statistics, the chi-squared distribution (also chi-square or χ²-distribution) with k degrees of freedom is the distribution of a sum of the squares of k independent standard normal random variables. It is a special case of the gamma distribution and is one of the most widely used probability distributions in inferential statistics, e.g., in hypothesis testing or in construction of confidence intervals.[1][2][3][4] When it is being distinguished from the more general noncentral chi-squared distribution, this distribution is sometimes called the central chi-squared distribution.
- ↑ Template:Abramowitz Stegun ref
- ↑ NIST (2006). Engineering Statistics Handbook - Chi-Squared Distribution
- ↑ Jonhson, N. L.; Kotz, S.; Balakrishnan, N. (1994). "Chi-Squared Distributions including Chi and Rayleigh". Continuous Univariate Distributions. 1 (Second ed.). John Willey and Sons. pp. 415–493. ISBN 0-471-58495-9.
- ↑ Mood, Alexander; Graybill, Franklin A.; Boes, Duane C. (1974). Introduction to the Theory of Statistics (Third ed.). McGraw-Hill. pp. 241–246. ISBN 0-07-042864-6.