Compute the variance of the variable V. More...

#include <STK_Stat_Functors.h>

Public Types
typedef Derived::Type	Type

Public Member Functions
	VarianceOp (ExprBase< Derived > const &V)
	constructor

Type const	operator() (bool unbiased) const

template<class Weights >
Type const	operator() (ExprBase< Weights > const &w, bool unbiased) const

Protected Attributes
Derived const &	V_

Detailed Description

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

Compute the variance of the variable V.

Definition at line 398 of file STK_Stat_Functors.h.

Member Typedef Documentation

◆ Type

template<class Derived >

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

Definition at line 400 of file STK_Stat_Functors.h.

Constructor & Destructor Documentation

◆ VarianceOp()

template<class Derived >

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

inline

constructor

Definition at line 402 of file STK_Stat_Functors.h.

402 : V_(V.asDerived())

403 { STK_STATIC_ASSERT_ONE_DIMENSION_ONLY(Derived);}

STK_STATIC_ASSERT_ONE_DIMENSION_ONLY

#define STK_STATIC_ASSERT_ONE_DIMENSION_ONLY(EXPR)

Definition STK_StaticAssert.h:151

STK::Stat::VarianceOp::V_

Derived const & V_

Definition STK_Stat_Functors.h:466

References STK_STATIC_ASSERT_ONE_DIMENSION_ONLY.

Member Function Documentation

◆ operator()() [1/2]

template<class Derived >

Type const STK::Stat::VarianceOp< Derived >::operator() ( bool unbiased ) const

inline

Returns: the variance of the variable V.
$\hat{\sigma}^2 = \frac{1}{n} \sum_{i=1}^n (V(i)-\hat{\mu})^2.$

Parameters

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

Definition at line 409 of file STK_Stat_Functors.h.

    {
      // no samples
      if (V_.empty()) { return Type(0);}
 
      int nobs = V_.size();
      // Compute the mean and sum
      Type mu = MeanOp<Derived>(V_)();
      Type sum  = 0.0, var  = 0.0, dev;
      for (int i=V_.begin(); i<V_.end(); i++)
      {
        sum += (dev = V_[i] - mu); // deviation from the mean
        var += (dev*dev);         // squared value
      }
      // compute the 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::VarianceOp< Derived >::V_.

◆ operator()() [2/2]

template<class Derived >

template<class Weights >

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

inline

Returns: the weighted variance of the variable V.
$\hat{\sigma}^2 = \frac{\sum_{i=1}^n w(i)}{\left( \sum_{i=1}^n w(i))\right)^2-\sum_{i=1}^n w(i)^2} \sum_{i=1}^n w(i) (V(i)-\hat{\mu})^2.$
If there is no weights, this definition reduces to the usual definition of the variance with factor 1/(n-1).

Parameters

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

Definition at line 443 of file STK_Stat_Functors.h.

    {
      STK_STATIC_ASSERT_ONE_DIMENSION_ONLY(Weights);
      // no samples
      if (V_.empty()) { return Type(0);}
      // Compute the mean
      Type mu = MeanOp<Derived>(V_)(w);
      // sum the weighted samples
      Type sum = 0.0, sum1weights= 0.0, sum2weights = 0.0;
      for (int i=V_.begin(); i<V_.end(); i++)
      {
        Type const weight = w[i];
        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) : Type(0)
      :
      (sum1weights) ? (sum/sum1weights) : Type(0);
    }