NormalSampler Class Reference

These tests are meant to use the bootstrap calculators and test against analytical confidence intervals. More...

Public Member Functions
	NormalSampler (Real mean, Real std, unsigned int seed)
Real	sample () const
std::vector< Real >	sample (std::size_t n) const
Real	meanConfidence (Real level, std::size_t n) const
Real	stdConfidence (Real level, std::size_t n) const

Static Private Member Functions
static Real	computeZ (Real level)

Private Attributes
const Real	_mean
const Real	_std
MooseRandom	_generator

Detailed Description

These tests are meant to use the bootstrap calculators and test against analytical confidence intervals.

The tolerance for the tests is pretty loose (50%), but at least it shows that the bootstrapping is in the ballpark (as it is meant to).

The analytical confidence intervals are based on sampling a normal distribution, this distributiong has nice properties so the confidence interval for mean and standard deviation are analytical.

• For mean, see https://en.wikipedia.org/wiki/Confidence_interval#Basic_steps
• For standard deviation, check out https://stats.stackexchange.com/questions/11707/why-is-sample-standard-deviation-a-biased-estimator-of-sigma/27984#27984

Definition at line 36 of file TestBootstrapCalculators.C.

Constructor & Destructor Documentation

NormalSampler()

NormalSampler::NormalSampler ( Real  mean, Real  std, unsigned int  seed  )

inline

Definition at line 39 of file TestBootstrapCalculators.C.

                                                        : _mean(mean), _std(std)
  {
    _generator.seed(seed);
  }

Member Function Documentation

computeZ()

static Real NormalSampler::computeZ ( Real  level )

inlinestaticprivate

Definition at line 70 of file TestBootstrapCalculators.C.

  {
    const Real alpha = level < 0.5 ? level : 1. - level;
    const Real z = -Normal::quantile(alpha / 2., 0, 1);
    return level < 0.5 ? -z : z;
  }

meanConfidence()

Real NormalSampler::meanConfidence ( Real  level, std::size_t  n  ) const

inline

Definition at line 53 of file TestBootstrapCalculators.C.

Referenced by TEST().

  {
    const Real z = computeZ(level);
    const Real mean_std = _std / std::sqrt(n);
    return z * mean_std;
  }

sample() [1/2]

Real NormalSampler::sample ( ) const

inline

Definition at line 44 of file TestBootstrapCalculators.C.

Referenced by TEST().

{ return _generator.randNormal(_mean, _std); }

sample() [2/2]

std::vector<Real> NormalSampler::sample ( std::size_t  n ) const

inline

Definition at line 45 of file TestBootstrapCalculators.C.

  {
    std::vector<Real> data(n);
    std::for_each(
        data.begin(), data.end(), [&](Real & v) { v = _generator.randNormal(_mean, _std); });
    return data;
  }

stdConfidence()

Real NormalSampler::stdConfidence ( Real  level, std::size_t  n  ) const

inline

Definition at line 60 of file TestBootstrapCalculators.C.

Referenced by TEST().

  {
    const Real z = computeZ(level);
    const Real nr = n;
    const Real gg = std::exp(std::lgamma(nr / 2.) - std::lgamma((nr - 1.) / 2.));
    const Real std_std = _std * std::sqrt(1.0 - 2. / (nr - 1.) * gg * gg);
    return z * std_std;
  }

Member Data Documentation

_generator

MooseRandom NormalSampler::_generator

private

Definition at line 79 of file TestBootstrapCalculators.C.

_mean

const Real NormalSampler::_mean

private

Definition at line 77 of file TestBootstrapCalculators.C.

_std

const Real NormalSampler::_std

private

Definition at line 78 of file TestBootstrapCalculators.C.

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

• stochastic_tools/unit/src/TestBootstrapCalculators.C