TruncatedNormalDistribution

Description

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

$(1)var element = document.getElementById("moose-equation-29b2ee21-8499-4961-a9f2-1b84361427a7");katex.render(" \\psi(x \\; | \\; \\mu, \\sigma^2, a, b) = \\begin{cases} \\frac{\\phi((x \\; | \\; \\mu, \\sigma^2)}{\\Phi(x\\;|\\;\\mu,\\sigma^2,b)-\\Phi(x\\;|\\;\\mu,\\sigma^2,a)},& \\text{if } a<x<b\\\\ 0, & \\text{otherwise} \\end{cases}", element, {displayMode:true,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$

The parameters $var element = document.getElementById("moose-equation-f98f9929-8dc2-45d7-a45b-5f8741a36d2b");katex.render("\\mu", element, {displayMode:false,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ and $var element = document.getElementById("moose-equation-6e1c9161-bf70-43d4-a6bb-d2b5831c5470");katex.render("\\sigma", element, {displayMode:false,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ are the mean and standard deviation of the general normal PDF. The $var element = document.getElementById("moose-equation-e1cdb5f7-0149-4426-827c-ae5fd3d762ae");katex.render("\\phi((x \\; | \\; \\mu, \\sigma^2)", element, {displayMode:false,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ and $var element = document.getElementById("moose-equation-23dc37bb-861e-4e5d-8362-908d7e7dacef");katex.render("\\Phi((x \\; | \\; \\mu, \\sigma^2)", element, {displayMode:false,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ are the general normal PDF and cumulative distribution function (CDF).

Example Input Syntax

The following input file defines a normal distribution with a mean of 0 and a standard deviation of 1 and truncation range (-10,10).

[Distributions]
  [normal_test]
    type = TruncatedNormalDistribution
    mean = 100
    standard_deviation = 25
    lower_bound = 50
    upper_bound = 150
  []
[]

/opt/civet/build_0/moose/modules/stochastic_tools/test/tests/distributions/truncated_normal.i

[Mesh]
  type = GeneratedMesh
  dim = 1
  nx = 1
  ny = 1
[]

[Variables]
  [u]
  []
[]

[Distributions]
  [normal_test]
    type = TruncatedNormalDistribution
    mean = 100
    standard_deviation = 25
    lower_bound = 50
    upper_bound = 150
  []
[]

[Postprocessors]
  [cdf]
    type = TestDistributionPostprocessor
    distribution = normal_test
    value = 137.962
    method = cdf
    execute_on = initial
  []
  [pdf]
    type = TestDistributionPostprocessor
    distribution = normal_test
    value = 137.962
    method = pdf
    execute_on = initial
  []
  [quantile]
    type = TestDistributionPostprocessor
    distribution = normal_test
    value = 0.956318
    method = quantile
    execute_on = initial
  []
[]

[Executioner]
  type = Steady
[]

[Problem]
  solve = false
  kernel_coverage_check = false
[]

[Outputs]
  execute_on = 'INITIAL'
  csv = true
[]

Input Parameters

meanMean (or expectation) of the distribution.
C++ Type:double
Options:
Description:Mean (or expectation) of the distribution.
standard_deviationStandard deviation of the distribution
C++ Type:double
Options:
Description:Standard deviation of the distribution

Required Parameters

lower_bound-1.79769e+308Lower bound of the distribution
Default:-1.79769e+308
C++ Type:double
Options:
Description:Lower bound of the distribution
upper_bound1.79769e+308Upper bound of the distribution
Default:1.79769e+308
C++ Type:double
Options:
Description:Upper bound of the distribution

Optional Parameters

control_tagsAdds user-defined labels for accessing object parameters via control logic.
C++ Type:std::vector
Options:
Description:Adds user-defined labels for accessing object parameters via control logic.
enableTrueSet the enabled status of the MooseObject.
Default:True
C++ Type:bool
Options:
Description:Set the enabled status of the MooseObject.

Advanced Parameters

Input Files

modules/stochastic_tools/test/tests/distributions/truncated_normal.i

modules/stochastic_tools/test/tests/distributions/truncated_normal.i

[Mesh]
  type = GeneratedMesh
  dim = 1
  nx = 1
  ny = 1
[]

[Variables]
  [u]
  []
[]

[Distributions]
  [normal_test]
    type = TruncatedNormalDistribution
    mean = 100
    standard_deviation = 25
    lower_bound = 50
    upper_bound = 150
  []
[]

[Postprocessors]
  [cdf]
    type = TestDistributionPostprocessor
    distribution = normal_test
    value = 137.962
    method = cdf
    execute_on = initial
  []
  [pdf]
    type = TestDistributionPostprocessor
    distribution = normal_test
    value = 137.962
    method = pdf
    execute_on = initial
  []
  [quantile]
    type = TestDistributionPostprocessor
    distribution = normal_test
    value = 0.956318
    method = quantile
    execute_on = initial
  []
[]

[Executioner]
  type = Steady
[]

[Problem]
  solve = false
  kernel_coverage_check = false
[]

[Outputs]
  execute_on = 'INITIAL'
  csv = true
[]

References

Description
Example Input Syntax
Input Parameters
Input Files
References

Application Usage

Physics and Syntax

Application Development

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