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: $var element = document.getElementById("moose-equation-2e5c4ceb-67e5-4b48-884d-eb5ef92b68b7");katex.render("\\gamma", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ , $var element = document.getElementById("moose-equation-de8181aa-11ec-437d-b909-5190da247c80");katex.render("\\delta", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ , $var element = document.getElementById("moose-equation-a88edf9e-1888-4fec-8d2d-62e93895fe13");katex.render("\\lambda", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ , and $var element = document.getElementById("moose-equation-0526c3e8-50ec-4bf7-bbb0-3fbc9704a655");katex.render("\\epsilon", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ . It is a continuous distribution defined on bounded range $var element = document.getElementById("moose-equation-dbed8623-7c78-4cdf-8155-332e2a592490");katex.render("\\epsilon \\leq x \\leq \\epsilon + \\lambda", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ , and the distribution can be symmetric or asymmetric.

Probability Density Function:

var element = document.getElementById("moose-equation-2e03c90f-db1c-4e01-bd8a-09a5f339611f");katex.render("f(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}", element, {displayMode:true,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});

Cumulative Density Function:

var element = document.getElementById("moose-equation-0002b718-5bd0-465d-a23b-c0bf86d9ca96");katex.render("F(x) = \\Phi(\\gamma + \\delta ln \\tfrac{z}{1-z}),\\,\\textrm{where}\\, z = \\tfrac{x-\\epsilon}{\\lambda}", element, {displayMode:true,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});

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>
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/johnsonsb.i)

Child Objects

(modules/stochastic_tools/include/distributions/JohnsonSBDistribution.h)

References

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

@book{johnson1994continuous,
    author = "Johnson, N. L. and Kotz, S. and Balakrishnan, N.",
    title = "Continuous Univariate Distributions",
    year = "1994",
    publisher = "Wiley",
    volume = "1",
    chapter = "12"
}

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

[StochasticTools]
[]

[Distributions]
  [johnsonsb_test]
    type = JohnsonSB
    a = 1
    b = 2
    alpha_1 = 1
    alpha_2 = 2
  []
[]

[Postprocessors]
  [cdf]
    type = TestDistributionPostprocessor
    distribution = johnsonsb_test
    value = 1.5
    method = cdf
    execute_on = initial
  []
  [pdf]
    type = TestDistributionPostprocessor
    distribution = johnsonsb_test
    value = 1.5
    method = pdf
    execute_on = initial
  []
  [quantile]
    type = TestDistributionPostprocessor
    distribution = johnsonsb_test
    value = 0.5
    method = quantile
    execute_on = initial
  []
[]

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

(modules/stochastic_tools/include/distributions/JohnsonSBDistribution.h)

// This file is part of the MOOSE framework
// https://mooseframework.inl.gov
//
// All rights reserved, see COPYRIGHT for full restrictions
// https://github.com/idaholab/moose/blob/master/COPYRIGHT
//
// Licensed under LGPL 2.1, please see LICENSE for details
// https://www.gnu.org/licenses/lgpl-2.1.html

#pragma once

#include "JohnsonSB.h"

/**
 * A deprecated wrapper class used to generate a Johnson SB distribution
 */
class JohnsonSBDistribution : public JohnsonSB
{
public:
  static InputParameters validParams();
  JohnsonSBDistribution(const InputParameters & parameters);
};

Description
Input Parameters
Input Files
Child Objects
References