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Statistics[Distributions][StudentT] - Student-t distribution
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Calling Sequence
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StudentT(nu)
StudentTDistribution(nu)
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Description
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The Student-t 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 StudentT variate is related to the Normal variate and the ChiSquare variate by the formula StudentT(nu) ~ Normal(0,1)/sqrt(ChiSquare(nu)/nu)
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The StudentT variate with degrees of freedom 1 is related to the standard Cauchy variate by StudentT(1) ~ Cauchy(0,1).
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Note that the StudentT command is inert and should be used in combination with the RandomVariable command.
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Examples
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![PIECEWISE([undefined, nu <= 1], [0, otherwise])](/support/helpjp/helpview.aspx?si=4660/file06600/math106.png)
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![PIECEWISE([undefined, nu <= 2], [nu/(-2+nu), otherwise])](/support/helpjp/helpview.aspx?si=4660/file06600/math113.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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