NormalDistribution Class Reference

A class used to generate a normal distribution. More...

#include <NormalDistribution.h>

Inheritance diagram for NormalDistribution:

Public Member Functions
	NormalDistribution (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 &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 &	_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 normal distribution.

Definition at line 22 of file NormalDistribution.h.

Constructor & Destructor Documentation

NormalDistribution()

NormalDistribution::NormalDistribution

(

const InputParameters &

parameters

)

Definition at line 35 of file NormalDistribution.C.

  : Distribution(parameters),
    _mean(getParam<Real>("mean")),
    _standard_deviation(getParam<Real>("standard_deviation"))
{
}

Member Function Documentation

cdf() [1/2]

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

overridevirtual

Reimplemented in JohnsonSBDistribution, and TruncatedNormalDistribution.

Definition at line 76 of file NormalDistribution.C.

{
  TIME_SECTION(_perf_cdf);
  return cdf(x, _mean, _standard_deviation);
}

Referenced by JohnsonSBDistribution::cdf(), TruncatedNormalDistribution::cdf(), TestDistributionDirectPostprocessor::getValue(), TruncatedNormalDistribution::pdf(), and TruncatedNormalDistribution::quantile().

cdf() [2/2]

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

static

Definition at line 50 of file NormalDistribution.C.

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

pdf() [1/2]

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

overridevirtual

Reimplemented in JohnsonSBDistribution, and TruncatedNormalDistribution.

Definition at line 69 of file NormalDistribution.C.

{
  TIME_SECTION(_perf_pdf);
  return pdf(x, _mean, _standard_deviation);
}

Referenced by TestDistributionDirectPostprocessor::getValue(), and TruncatedNormalDistribution::pdf().

pdf() [2/2]

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

static

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() [1/2]

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

overridevirtual

Reimplemented in JohnsonSBDistribution, and TruncatedNormalDistribution.

Definition at line 83 of file NormalDistribution.C.

{
  TIME_SECTION(_perf_quantile);
  return quantile(p, _mean, _standard_deviation);
}

Referenced by TestDistributionDirectPostprocessor::getValue(), JohnsonSBDistribution::quantile(), and TruncatedNormalDistribution::quantile().

quantile() [2/2]

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

static

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 NormalDistribution::validParams ( )

static

Definition at line 25 of file NormalDistribution.C.

{
  InputParameters params = Distribution::validParams();
  params.addClassDescription("Normal distribution");
  params.addRequiredParam<Real>("mean", "Mean (or expectation) of the distribution.");
  params.addRequiredRangeCheckedParam<Real>(
      "standard_deviation", "standard_deviation > 0", "Standard deviation of the distribution ");
  return params;
}

Referenced by JohnsonSBDistribution::validParams(), and TruncatedNormalDistribution::validParams().

Member Data Documentation

_a

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

staticprotected

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 quantile().

_b

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

staticprotected

Initial value:

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

Definition at line 41 of file NormalDistribution.h.

Referenced by quantile().

_mean

const Real& NormalDistribution::_mean

protected

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

Definition at line 45 of file NormalDistribution.h.

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

_standard_deviation

const Real& NormalDistribution::_standard_deviation

protected

The standard deviation of the distribution (sigma)

Definition at line 48 of file NormalDistribution.h.

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

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

• stochastic_tools/include/distributions/NormalDistribution.h
• stochastic_tools/src/distributions/NormalDistribution.C