Gamma Distribution

Gamma distribution

Overview

This object defines a gamma distribution with "shape" parameter ( or ) and "scale" parameter ( or ). The probability density function, cumulative distribution function, and quantile are defined in Eq. (1), Eq. (2), and Eq. (3), respectively.

(1)(2)(3)

where and . is the gamma function defined by Eq. (4), is the lower incomplete gamma function defined by Eq. (5), and is the inverse of the incomplete gamma function. and are computed using a custom iterative procedure, which obtains an accuracy of about .

(4)(5)

Input Parameters

  • shapeShape parameter (k or alpha).

    C++ Type:double

    Unit:(no unit assumed)

    Controllable:No

    Description:Shape parameter (k or alpha).

Required Parameters

  • scale1Scale parameter (theta or 1/beta).

    Default:1

    C++ Type:double

    Unit:(no unit assumed)

    Controllable:No

    Description:Scale parameter (theta or 1/beta).

Optional 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