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Statistics[Distributions][ChiSquare] - chi-square distribution
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Calling Sequence
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ChiSquare(nu)
ChiSquareDistribution(nu)
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Description
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The chi-square distribution is a continuous probability distribution with probability density function given by:
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subject to the following conditions:
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The ChiSquare variate with nu degrees of freedom is equivalent to the Gamma variate with scale  and shape nu/2: ChiSquare(nu) ~ Gamma(2,nu/2).
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The ChiSquare variate is related to the FRatio variate by the formula FRatio(nu,omega) ~ (ChiSquare(nu)*omega)/(ChiSquare(omega)*nu)
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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)
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Note that the ChiSquare command is inert and should be used in combination with the RandomVariable command.
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Examples
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![PIECEWISE([0, u < 0], [u^((1/2)*nu-1)*exp(-(1/2)*u)/(2^((1/2)*nu)*GAMMA((1/2)*nu)), otherwise])](/support/helpjp/helpview.aspx?si=4628/file06572/math107.png)
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References
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Evans, Merran; Hastings, Nicholas; and Peacock, Brian. Statistical Distributions. 3rd ed. Hoboken: Wiley, 2000.
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Johnson, Norman L.; Kotz, Samuel; and Balakrishnan, N. Continuous Univariate Distributions. 2nd ed. 2 vols. Hoboken: Wiley, 1995.
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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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