Student t-distribution

Overview

This object defines a student t-distribution with one degree of freedom parameter "dof" ( $var element = document.getElementById("moose-equation-c7f6f4a3-2d8b-4bff-98dd-461ab02e2999");katex.render("\\nu", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ ). The probability density function and cumulative distribution function are defined in Eq. (1) and Eq. (2), respectively.

(1)var element = document.getElementById("moose-equation-a4f00b8d-7643-467c-a6b4-a4e5b7015e07");katex.render("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}},", element, {displayMode:true,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});

(2)var element = document.getElementById("moose-equation-8784af76-a0a4-497b-85a7-677101fb3e2e");katex.render("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},", element, {displayMode:true,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});

where $var element = document.getElementById("moose-equation-709e8a0e-821e-4704-8920-e31240c9bf42");katex.render("\\nu \\in \\mathbb{Z} > 0", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ . $var element = document.getElementById("moose-equation-2aabd4f0-2c73-49ab-8705-bee097d3a952");katex.render("\\Beta(a,b)", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ is the beta function and $var element = document.getElementById("moose-equation-d23232a0-68cf-4ce6-9efc-11a32c87dae6");katex.render("I_z(a,b)", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ is the regularized incomplete beta function, see Beta Distribution for more details.

Input Parameters

dofDegrees of freedom.
C++ Type:unsigned int
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>
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
Controllable:No
Description:Set the enabled status of the MooseObject.

Advanced Parameters

Input Files

(modules/stochastic_tools/test/tests/distributions/studentt.i)

(modules/stochastic_tools/test/tests/distributions/studentt.i)

[StochasticTools]
[]

[Distributions]
  [studentt]
    type = StudentT
    dof = 17
  []
[]

[Postprocessors]
  [cdf1]
    type = TestDistributionPostprocessor
    distribution = studentt
    value = 0.39548722930287195
    method = cdf
    execute_on = initial
  []
  [cdf2]
    type = TestDistributionPostprocessor
    distribution = studentt
    value = -3.323540778359423
    method = cdf
    execute_on = initial
  []
  [pdf1]
    type = TestDistributionPostprocessor
    distribution = studentt
    value = 0.39548722930287195
    method = pdf
    execute_on = initial
  []
  [pdf2]
    type = TestDistributionPostprocessor
    distribution = studentt
    value = -3.323540778359423
    method = pdf
    execute_on = initial
  []
  [quantile1]
    type = TestDistributionPostprocessor
    distribution = studentt
    value = 0.17746982321896032
    method = quantile
    execute_on = initial
  []
  [quantile2]
    type = TestDistributionPostprocessor
    distribution = studentt
    value = 0.897910497498433
    method = quantile
    execute_on = initial
  []
[]

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

Overview
Input Parameters
Input Files