F-Distribution

F-distribution or Fisher-Snedecor distribution

Overview

This object defines a F-distribution with two degree of freedom parameters: "df1" (d1d_1) and "df2" (d2d_2). The probability density function and cumulative distribution function are defined in Eq. (1) and Eq. (2), respectively.

f(x;d1,d2)=1B(d12,d22)(d1d2)d12xd121(1+d1d2x)d1d22,f(x; d_1, d_2) = \frac{1}{\Beta\left(\frac{d_1}{2},\frac{d_2}{2}\right)} \left(\frac{d_1}{d_2}\right)^{\frac{d_1}{2}} x^{\frac{d_1}{2}-1} \left(1+\frac{d_1}{d_2}x\right)^{-\frac{d_1-d_2}{2}},(1)F(x;d1,d2)=Iz(x)(d12,d22),z(x)=d1xd1x+d2,F(x; d_1, d_2) = I_{z(x)}\left(\frac{d_1}{2},\frac{d_2}{2}\right), \quad z(x) = \frac{d_1x}{d_1x+d_2},(2)

where d1,d2Z>0d_1,d_2 \in \mathbb{Z} > 0 and x>0x > 0. B(a,b)\Beta(a,b) is the beta function and Iz(a,b)I_z(a,b) is the regularized incomplete beta function, see Beta Distribution for more details.

Input Parameters

  • df1Degrees of freedom 1.

    C++ Type:unsigned int

    Unit:(no unit assumed)

    Controllable:No

    Description:Degrees of freedom 1.

  • df2Degrees of freedom 2.

    C++ Type:unsigned int

    Unit:(no unit assumed)

    Controllable:No

    Description:Degrees of freedom 2.

Required Parameters

  • control_tagsAdds user-defined labels for accessing object parameters via control logic.

    C++ Type:std::vector<std::string>

    Unit:(no unit assumed)

    Controllable:No

    Description:Adds user-defined labels for accessing object parameters via control logic.

  • enableTrueSet the enabled status of the MooseObject.

    Default:True

    C++ Type:bool

    Unit:(no unit assumed)

    Controllable:No

    Description:Set the enabled status of the MooseObject.

Advanced Parameters