Chi-square distribution

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In probability theory and statistics, the chi-square distribution (also chi-squared or   distribution) is one of the most widely used theoretical probability distributions. Chi-square distribution with degrees of freedom is written as .[1] It is a special case of gamma distribution.[2]

Chi-square distribution is primarily used in statistical significance tests and confidence intervals.[3] It is useful, because it is relatively easy to show that certain probability distributions come close to it, under certain conditions. One of these conditions is that the null hypothesis must be true. Another one is that the different random variables (or observations) must be independent of each other.

Related pages[change | change source]

References[change | change source]

  1. "List of Probability and Statistics Symbols". Math Vault. 2020-04-26. Retrieved 2020-09-14.
  2. Weisstein, Eric W. "Chi-Squared Distribution". mathworld.wolfram.com. Retrieved 2020-09-14.
  3. "1.3.6.6.6. Chi-Square Distribution". www.itl.nist.gov. Retrieved 2020-09-14.
chi-square
Probability density function
Chi-square distributionPDF.png
Cumulative distribution function
Chi-square distributionCDF.png
Parameters degrees of freedom
Support
Probability density function (pdf)
Cumulative distribution function (cdf)
Mean
Median approximately
Mode if
Variance
Skewness
Excess kurtosis
Entropy
Moment-generating function (mgf) for
Characteristic function

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