Student t-distribution

Student t-distribution

Overview

This object defines a student t-distribution with one degree of freedom parameter "dof" (ν\nu). The probability density function and cumulative distribution function are defined in Eq. (1) and Eq. (2), respectively.

f(x;ν)=1νB(12,ν2)(1+x2ν)ν+12,f(x; \nu) = \frac{1}{\sqrt{\nu}\Beta\left(\frac{1}{2},\frac{\nu}{2}\right)} \left(1+\frac{x^2}{\nu}\right)^{-\frac{\nu+1}{2}},(1)F(x;ν)=112Iz(x)(ν2,12),z(x)=νx2+ν,F(x; \nu) = 1 - \frac{1}{2}I_{z(x)}\left(\frac{\nu}{2},\frac{1}{2}\right), \quad z(x) = \frac{\nu}{x^2+\nu},(2)

where νZ>0\nu \in \mathbb{Z} > 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

  • dofDegrees of freedom.

    C++ Type:unsigned int

    Unit:(no unit assumed)

    Controllable:No

    Description:Degrees of freedom.

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