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Statistics[Distributions][FRatio] - f-ratio distribution
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Calling Sequence
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FRatio(nu, omega)
FRatioDistribution(nu, omega)
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Parameters
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nu
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first degrees of freedom parameter
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omega
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second degrees of freedom parameter
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Description
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The f-ratio 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 FRatio variate is related to independent ChiSquare variates with degrees of freedom nu and omega by the formula FRatio(nu,omega) ~ (ChiSquare(nu)*omega)/(ChiSquare(omega)*nu)
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The FRatio variate is related to independent Laplace variates with location parameter 0 and scale parameter b by the formula FRatio(2,2) ~ abs(Laplace(0,b))/abs(Laplace(0,b))
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Note that the FRatio 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], [GAMMA((1/2)*nu+(1/2)*omega)*(nu/omega)^((1/2)*nu)*u^((1/2)*nu-1)/(GAMMA((1/2)*nu)*GAMMA((1/2)*omega)*(1+nu*u/omega)^((1/2)*nu+(1/2)*omega)), otherwise])](/support/helpjp/helpview.aspx?si=4646/file06578/math107.png)
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![PIECEWISE([undefined, omega <= 2], [omega/(-2+omega), otherwise])](/support/helpjp/helpview.aspx?si=4646/file06578/math121.png)
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![PIECEWISE([undefined, omega <= 4], [2*omega^2*(nu+omega-2)/(nu*(-2+omega)^2*(-4+omega)), otherwise])](/support/helpjp/helpview.aspx?si=4646/file06578/math128.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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