The chi-square distribution is a continuous probability distribution with probability density function given by:
subject to the following conditions:
The ChiSquare variate with nu degrees of freedom is equivalent to the Gamma variate with scale 2 and shape nu/2: ChiSquare(nu) ~ Gamma(2,nu/2).
The ChiSquare variate is related to the FRatio variate by the formula FRatio(nu,omega) ~ (ChiSquare(nu)*omega)/(ChiSquare(omega)*nu)
The ChiSquare variate is related to the Normal variate and the StudentT variate by the formula StudentT(nu) ~ Normal(0,1)/sqrt(ChiSquare(nu)/nu)
Note that the ChiSquare command is inert and should be used in combination with the RandomVariable command.
X ≔ RandomVariable⁡ChiSquare⁡ν:
Evans, Merran; Hastings, Nicholas; and Peacock, Brian. Statistical Distributions. 3rd ed. Hoboken: Wiley, 2000.
Johnson, Norman L.; Kotz, Samuel; and Balakrishnan, N. Continuous Univariate Distributions. 2nd ed. 2 vols. Hoboken: Wiley, 1995.
Stuart, Alan, and Ord, Keith. Kendall's Advanced Theory of Statistics. 6th ed. London: Edward Arnold, 1998. Vol 1: Distribution Theory.
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