A class used to generate a Johnson SB distribution. More...

#include <JohnsonSBDistribution.h>

Inheritance diagram for JohnsonSBDistribution:

Public Member Functions
	JohnsonSBDistribution (const InputParameters &parameters)

virtual Real	pdf (const Real &x) const override

virtual Real	cdf (const Real &x) const override

virtual Real	quantile (const Real &p) const override

Static Public Member Functions
static InputParameters	validParams ()

static Real	pdf (const Real &x, const Real &a, const Real &b, const Real &alpha_1, const Real &alpha_2)

static Real	cdf (const Real &x, const Real &a, const Real &b, const Real &alpha_1, const Real &alpha_2)

static Real	quantile (const Real &p, const Real &a, const Real &b, const Real &alpha_1, const Real &alpha_2)

static Real	pdf (const Real &x, const Real &mean, const Real &std_dev)

static Real	cdf (const Real &x, const Real &mean, const Real &std_dev)

static Real	quantile (const Real &p, const Real &mean, const Real &std_dev)

Protected Attributes
const Real &	_lower
	The lower location parameter, a. More...

const Real &	_upper
	The upper location parameter, b. More...

const Real &	_alpha_1
	The first shape parameter, alpha_1. More...

const Real &	_alpha_2
	The second shape parameter, alpha_2. More...

const Real &	_mean
	The mean (or expectation) of the distribution (mu) More...

const Real &	_standard_deviation
	The standard deviation of the distribution (sigma) More...

Static Protected Attributes

static const std::array< Real, 6 >	_a

static const std::array< Real, 6 >	_b

Detailed Description

A class used to generate a Johnson SB distribution.

Definition at line 22 of file JohnsonSBDistribution.h.

Constructor & Destructor Documentation

◆ JohnsonSBDistribution()

JohnsonSBDistribution::JohnsonSBDistribution ( const InputParameters & parameters )

Definition at line 37 of file JohnsonSBDistribution.C.

   : NormalDistribution(parameters),
     _lower(getParam<Real>("a")),
     _upper(getParam<Real>("b")),
     _alpha_1(getParam<Real>("alpha_1")),
     _alpha_2(getParam<Real>("alpha_2"))
 {
 }

Member Function Documentation

◆ cdf() [1/3]

Real JohnsonSBDistribution::cdf ( const Real & x ) const

overridevirtual

Reimplemented from NormalDistribution.

Definition at line 91 of file JohnsonSBDistribution.C.

 {
   TIME_SECTION(_perf_cdf);
   return cdf(x, _lower, _upper, _alpha_1, _alpha_2);
 }

◆ cdf() [2/3]

Real JohnsonSBDistribution::cdf	(	const Real &	x,
		const Real &	a,
		const Real &	b,
		const Real &	alpha_1,
		const Real &	alpha_2
	)

static

Definition at line 62 of file JohnsonSBDistribution.C.

 {
   if (x <= a)
     return 0.0;
   else if (x < b)
   {
     return NormalDistribution::cdf(alpha_1 + alpha_2 * std::log((x - a) / (b - x)), 0.0, 1.0);
   }
   else
     return 0.0;
 }

◆ cdf() [3/3]

Real NormalDistribution::cdf	(	const Real &	x,
		const Real &	mean,
		const Real &	std_dev
	)

staticinherited

Definition at line 50 of file NormalDistribution.C.

 {
   return 0.5 * (1.0 + std::erf((x - mean) / (std_dev * std::sqrt(2.0))));
 }

◆ pdf() [1/3]

Real JohnsonSBDistribution::pdf ( const Real & x ) const

overridevirtual

Reimplemented from NormalDistribution.

Definition at line 84 of file JohnsonSBDistribution.C.

 {
   TIME_SECTION(_perf_pdf);
   return pdf(x, _lower, _upper, _alpha_1, _alpha_2);
 }

◆ pdf() [2/3]

Real JohnsonSBDistribution::pdf	(	const Real &	x,
		const Real &	a,
		const Real &	b,
		const Real &	alpha_1,
		const Real &	alpha_2
	)

static

Definition at line 47 of file JohnsonSBDistribution.C.

 {
   if (x <= a)
     return 0.0;
   else if (x < b)
   {
     return (alpha_2 * (b - a)) / ((x - a) * (b - x) * std::sqrt(2.0 * M_PI)) *
            std::exp(-0.5 * Utility::pow<2>(alpha_1 + alpha_2 * std::log((x - a) / (b - x))));
   }
   else
     return 0.0;
 }

◆ pdf() [3/3]

Real NormalDistribution::pdf	(	const Real &	x,
		const Real &	mean,
		const Real &	std_dev
	)

staticinherited

Definition at line 43 of file NormalDistribution.C.

 {
   return 1.0 / (std_dev * std::sqrt(2.0 * M_PI)) *
          std::exp(-0.5 * Utility::pow<2>((x - mean) / std_dev));
 }

◆ quantile() [1/3]

Real JohnsonSBDistribution::quantile ( const Real & p ) const

overridevirtual

Reimplemented from NormalDistribution.

Definition at line 98 of file JohnsonSBDistribution.C.

 {
   TIME_SECTION(_perf_quantile);
   return quantile(p, _lower, _upper, _alpha_1, _alpha_2);
 }

◆ quantile() [2/3]

Real JohnsonSBDistribution::quantile	(	const Real &	p,
		const Real &	a,
		const Real &	b,
		const Real &	alpha_1,
		const Real &	alpha_2
	)

static

Definition at line 76 of file JohnsonSBDistribution.C.

 {
   const Real Z = NormalDistribution::quantile(p, 0.0, 1.0);
   return (a + b * std::exp((Z - alpha_1) / alpha_2)) / (1.0 + std::exp((Z - alpha_1) / alpha_2));
 }

◆ quantile() [3/3]

Real NormalDistribution::quantile	(	const Real &	p,
		const Real &	mean,
		const Real &	std_dev
	)

staticinherited

Definition at line 56 of file NormalDistribution.C.

 {
   Real x = (p < 0.5 ? p : 1.0 - p);
   Real y = std::sqrt(-2.0 * std::log(x));
   Real sgn = (p - 0.5 < 0.0 ? -1.0 : 1.0);
   Real Zp = sgn * (y + (_a[0] + _a[1] * y + _a[2] * Utility::pow<2>(y) +
                         _a[3] * Utility::pow<3>(y) + _a[4] * Utility::pow<4>(y)) /
                            (_b[0] + _b[1] * y + _b[2] * Utility::pow<2>(y) +
                             _b[3] * Utility::pow<3>(y) + _b[4] * Utility::pow<4>(y)));
   return Zp * std_dev + mean;
 }

◆ validParams()

InputParameters JohnsonSBDistribution::validParams ( )

static

Definition at line 19 of file JohnsonSBDistribution.C.

 {
   InputParameters params = NormalDistribution::validParams();
   params.addClassDescription("Johnson Special Bounded (SB) distribution.");
  
   params.set<Real>("mean") = 0.0;
   params.set<Real>("standard_deviation") = 1.0;
   params.suppressParameter<Real>("mean");
   params.suppressParameter<Real>("standard_deviation");
  
   params.addRequiredParam<Real>("a", "Lower location parameter");
   params.addRequiredParam<Real>("b", "Upper location parameter");
   params.addRequiredParam<Real>("alpha_1", "Shape parameter (sometimes called a)");
   params.addRequiredParam<Real>("alpha_2", "Shape parameter (sometimes called b)");
  
   return params;
 }

Member Data Documentation

◆ _a

const std::array< Real, 6 > NormalDistribution::_a

staticprotectedinherited

Initial value:

= {

{-0.322232431088, -1.0, -0.342242088547, -0.0204231210245, -0.0000453642210148}}

Coefficients for the rational function used to approximate the quantile

Definition at line 40 of file NormalDistribution.h.

Referenced by NormalDistribution::quantile().

◆ _alpha_1

const Real& JohnsonSBDistribution::_alpha_1

protected

The first shape parameter, alpha_1.

Definition at line 48 of file JohnsonSBDistribution.h.

Referenced by cdf(), pdf(), and quantile().

◆ _alpha_2

const Real& JohnsonSBDistribution::_alpha_2

protected

The second shape parameter, alpha_2.

Definition at line 51 of file JohnsonSBDistribution.h.

Referenced by cdf(), pdf(), and quantile().

◆ _b

const std::array< Real, 6 > NormalDistribution::_b

staticprotectedinherited

Initial value:

= {

{0.099348462606, 0.588581570495, 0.531103462366, 0.10353775285, 0.0038560700634}}

Definition at line 41 of file NormalDistribution.h.

Referenced by NormalDistribution::quantile().

◆ _lower

const Real& JohnsonSBDistribution::_lower

protected

The lower location parameter, a.

Definition at line 42 of file JohnsonSBDistribution.h.

Referenced by cdf(), pdf(), and quantile().

◆ _mean

const Real& NormalDistribution::_mean

protectedinherited

The mean (or expectation) of the distribution (mu)

Definition at line 45 of file NormalDistribution.h.

Referenced by NormalDistribution::cdf(), TruncatedNormalDistribution::cdf(), NormalDistribution::pdf(), TruncatedNormalDistribution::pdf(), NormalDistribution::quantile(), and TruncatedNormalDistribution::quantile().

◆ _standard_deviation

const Real& NormalDistribution::_standard_deviation

protectedinherited

The standard deviation of the distribution (sigma)

Definition at line 48 of file NormalDistribution.h.

Referenced by NormalDistribution::cdf(), TruncatedNormalDistribution::cdf(), NormalDistribution::pdf(), TruncatedNormalDistribution::pdf(), NormalDistribution::quantile(), and TruncatedNormalDistribution::quantile().

◆ _upper

const Real& JohnsonSBDistribution::_upper

protected

The upper location parameter, b.

Definition at line 45 of file JohnsonSBDistribution.h.

Referenced by cdf(), pdf(), and quantile().

The documentation for this class was generated from the following files:

stochastic_tools/include/distributions/JohnsonSBDistribution.h
stochastic_tools/src/distributions/JohnsonSBDistribution.C

Public Member Functions

Static Public Member Functions

Protected Attributes

Static Protected Attributes

Detailed Description

Constructor & Destructor Documentation

◆ JohnsonSBDistribution()

Member Function Documentation

◆ cdf() [1/3]

◆ cdf() [2/3]

◆ cdf() [3/3]

◆ pdf() [1/3]

◆ pdf() [2/3]

◆ pdf() [3/3]

◆ quantile() [1/3]

◆ quantile() [2/3]

◆ quantile() [3/3]

◆ validParams()

Member Data Documentation

◆ _a

◆ _alpha_1

◆ _alpha_2

◆ _b

◆ _lower

◆ _mean

◆ _standard_deviation

◆ _upper