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Chi-squared distribution
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=== Gamma, exponential, and related distributions === The chi-squared distribution <math>X \sim \chi_k^2</math> is a special case of the [[gamma distribution]], in that <math>X \sim \Gamma \left(\frac{k}2,\frac{1}2\right)</math> using the rate parameterization of the gamma distribution (or <math>X \sim \Gamma \left(\frac{k}2,2 \right)</math> using the scale parameterization of the gamma distribution) where {{mvar|k}} is an integer. Because the [[exponential distribution]] is also a special case of the gamma distribution, we also have that if <math>X \sim \chi_2^2</math>, then <math>X\sim \operatorname{exp}\left(\frac 1 2\right)</math> is an [[exponential distribution]]. The [[Erlang distribution]] is also a special case of the gamma distribution and thus we also have that if <math>X \sim\chi_k^2</math> with even <math>k</math>, then <math>X</math> is Erlang distributed with shape parameter <math>k/2</math> and scale parameter <math>1/2</math>.
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