JohnsonSB

Johnson Special Bounded (SB) distribution.

Description

The Johnson Special Bounded (SB) distribution Johnson et al. (1994) is related to the normal distribution. Four parameters are needed: γ\gamma, δ\delta, λ\lambda, and ϵ\epsilon. It is a continuous distribution defined on bounded range ϵxϵ+λ\epsilon \leq x \leq \epsilon + \lambda, and the distribution can be symmetric or asymmetric.

Probability Density Function:

f(x)=δλ2πz(1z)exp(12(γ+δln(z1z))2),wherezxζλf(x) = \tfrac{\delta}{\lambda\sqrt{2\pi} z(1-z)} exp(-\tfrac{1}{2}(\gamma + \delta ln(\tfrac{z}{1-z}))^2),\,\textrm{where}\, z \equiv \tfrac{x-\zeta}{\lambda}

Cumulative Density Function:

F(x)=Φ(γ+δlnz1z),wherez=xϵλF(x) = \Phi(\gamma + \delta ln \tfrac{z}{1-z}),\,\textrm{where}\, z = \tfrac{x-\epsilon}{\lambda}

Input Parameters

  • aLower location parameter

    C++ Type:double

    Unit:(no unit assumed)

    Controllable:No

    Description:Lower location parameter

  • alpha_1Shape parameter (sometimes called a)

    C++ Type:double

    Unit:(no unit assumed)

    Controllable:No

    Description:Shape parameter (sometimes called a)

  • alpha_2Shape parameter (sometimes called b)

    C++ Type:double

    Unit:(no unit assumed)

    Controllable:No

    Description:Shape parameter (sometimes called b)

  • bUpper location parameter

    C++ Type:double

    Unit:(no unit assumed)

    Controllable:No

    Description:Upper location parameter

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

References

  1. N. L. Johnson, S. Kotz, and N. Balakrishnan. Continuous Univariate Distributions. Volume 1. Wiley, 1994.[BibTeX]