Normal

Normal distribution

Description

The normal (or Gaussian) distribution object defines a normal distribution function with the provided mean and standard_deviation parameters. The probability density function (PDF) of the normal distribution is given by the Eq. (1).

f(x    μ,σ2)=12πσ2  e(xμ)22σ2f(x \; | \; \mu, \sigma^2) = \frac{1}{\sqrt{2\pi\sigma^2} } \; e^{ -\frac{(x-\mu)^2}{2\sigma^2} }(1)

where μ\mu is the mean and σ\sigma is the standard deviation (σ>0\sigma > 0) of the distribution.

This implementation of a normal distribution uses a numerical approximation described in Kennedy and Gentle (2018).

Example Input Syntax

The following input file defines a normal distribution with a mean of 0 and a standard deviation of 1.

[Distributions]
  [normal_test]
    type = Normal
    mean = 0
    standard_deviation = 1
  []
[]
(contrib/moose/modules/stochastic_tools/test/tests/distributions/normal.i)

Input Parameters

  • meanMean (or expectation) of the distribution.

    C++ Type:double

    Unit:(no unit assumed)

    Controllable:No

    Description:Mean (or expectation) of the distribution.

  • standard_deviationStandard deviation of the distribution

    C++ Type:double

    Unit:(no unit assumed)

    Controllable:No

    Description:Standard deviation of the distribution

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. William J Kennedy and James E Gentle. Statistical computing. Routledge, 2018.[BibTeX]