STK::Stat::VarianceWithFixedMeanOp< Derived > Struct Template Reference

Compute the variance of the variable V when the mean is given. More...

#include <STK_Stat_Functors.h>

Public Types
typedef Derived::Type	Type

Public Member Functions
	VarianceWithFixedMeanOp (ExprBase< Derived > const &V)
	constructor
Type const	operator() (Type const &mu, bool unbiased) const
template<class Weights >
Type const	operator() (ExprBase< Weights > const &w, Type const &mu, bool unbiased) const

Protected Attributes
Derived const &	V_

Detailed Description

template<class Derived>
struct STK::Stat::VarianceWithFixedMeanOp< Derived >

Compute the variance of the variable V when the mean is given.

Definition at line 558 of file STK_Stat_Functors.h.

Member Typedef Documentation

Type

template<class Derived >

typedef Derived::Type STK::Stat::VarianceWithFixedMeanOp< Derived >::Type

Definition at line 560 of file STK_Stat_Functors.h.

Constructor & Destructor Documentation

VarianceWithFixedMeanOp()

template<class Derived >

STK::Stat::VarianceWithFixedMeanOp< Derived >::VarianceWithFixedMeanOp ( ExprBase< Derived > const &  V )

inline

constructor

Definition at line 562 of file STK_Stat_Functors.h.

                                                               :  V_(V.asDerived())
  { STK_STATIC_ASSERT_ONE_DIMENSION_ONLY(Derived);}

References STK_STATIC_ASSERT_ONE_DIMENSION_ONLY.

Member Function Documentation

operator()() [1/2]

template<class Derived >

template<class Weights >

Type const STK::Stat::VarianceWithFixedMeanOp< Derived >::operator() ( ExprBase< Weights > const &  w, Type const &  mu, bool  unbiased  ) const

inline

Returns

the weighted variance of the variable V with fixed mean.

In the unbiased case, the method use the compensated method described in http://en.wikipedia.org/wiki/Weighted_arithmetic_mean#Weighted_sample_variance

Parameters

w	weights
mu	the mean
unbiased	true if we want an unbiased estimate of the variance, false otherwise

Definition at line 606 of file STK_Stat_Functors.h.

    {
      STK_STATIC_ASSERT_ONE_DIMENSION_ONLY(Weights);
      // no samples
      if (V_.empty()) { return Type(0);}
      // sum the weighted samples
      Type sum = 0.0, sum1weights = 0.0, sum2weights = 0.0;
      for (int i=V_.begin(); i<V_.end(); i++)
      {
        Real weight = std::abs(w[i]); // only positive weights
        sum1weights += weight;
        sum2weights += weight * weight;
        sum         += weight * (V_[i]-mu)*(V_[i]-mu);  // deviation from the mean
      }
      // compute the variance
      return (unbiased) ?
      (sum1weights) ?  (sum)/(sum1weights - sum2weights/sum1weights)
                    : Arithmetic<Type>::infinity()
      :
      (sum1weights) ? (sum/sum1weights) : Type(0);
    }

References STK_STATIC_ASSERT_ONE_DIMENSION_ONLY, STK::Stat::sum(), and STK::Stat::VarianceWithFixedMeanOp< Derived >::V_.

operator()() [2/2]

template<class Derived >

Type const STK::Stat::VarianceWithFixedMeanOp< Derived >::operator() ( Type const &  mu, bool  unbiased  ) const

inline

Returns

the variance of the variable V with fixed mean.

using a compensated algorithm.

Note

Chan, Tony F.; Golub, Gene H.; LeVeque, Randall J. (1983). Algorithms for Computing the Sample Variance: Analysis and Recommendations. The American Statistician 37, 242-247.

Parameters

mu	the fixed mean
unbiased	true if we want an unbiased estimate of the variance, false otherwise

Definition at line 575 of file STK_Stat_Functors.h.

    {
      // no samples
      if (V_.empty()) { return Type(0);}
      int nobs = V_.size();
      // sum
      Type sum = 0., var = 0., dev;
      for (int i=V_.begin(); i<V_.end(); i++)
      {
        sum += (dev = V_[i] - mu); // deviation from the mean
        var += (dev*dev);         // squared value
      }
      // unbiased variance
      return (unbiased) ?
      (nobs > 1) ? (var - (sum*sum)/(Type)(nobs))/((Type)nobs -1)
                 : Arithmetic<Type>::infinity()
      :
      (nobs > 0) ? (var - (sum*sum)/Type(nobs))/Type(nobs) : Type(0);
    }

References STK::Stat::sum(), and STK::Stat::VarianceWithFixedMeanOp< Derived >::V_.

Member Data Documentation

V_

template<class Derived >

Derived const& STK::Stat::VarianceWithFixedMeanOp< Derived >::V_

protected

Definition at line 628 of file STK_Stat_Functors.h.

Referenced by STK::Stat::VarianceWithFixedMeanOp< Derived >::operator()(), and STK::Stat::VarianceWithFixedMeanOp< Derived >::operator()().

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

• STK_Stat_Functors.h