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

#include <STK_Stat_Functors.h>

Public Types
typedef Derived::Type	Type

Public Member Functions
	VarianceSafeOp (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::VarianceSafeOp< Derived >

Compute safely the variance of the variable V.

Definition at line 473 of file STK_Stat_Functors.h.

Member Typedef Documentation

◆ Type

template<class Derived >

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

Definition at line 475 of file STK_Stat_Functors.h.

Constructor & Destructor Documentation

◆ VarianceSafeOp()

template<class Derived >

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

inline

constructor

Definition at line 477 of file STK_Stat_Functors.h.

477 : V_(V.asDerived())

478 { 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::VarianceSafeOp::V_

Derived const & V_

Definition STK_Stat_Functors.h:551

References STK_STATIC_ASSERT_ONE_DIMENSION_ONLY.

Member Function Documentation

◆ operator()() [1/2]

template<class Derived >

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

inline

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

Parameters

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

Definition at line 484 of file STK_Stat_Functors.h.

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

◆ operator()() [2/2]

template<class Derived >

template<class Weights >

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

inline

Returns: the safely computed 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 522 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 = MeanSafeOp<Derived>(V_)(w);
#ifdef STK_BOUNDS_CHECK
      if (V_.range() != w.range())
        STKRUNTIME_ERROR_NO_ARG(VarianceSafeOp,V.range()!=w.range());
#endif
      // sum the weighted samples
      Type sum = 0.0, sum1weights= 0.0, sum2weights = 0.0;
      for (int i=V_.begin(); i<V_.end(); i++)
      { if ( !Arithmetic<Type>::isNA(V_[i]) && !Arithmetic<Type>::isNA(w[i]) )
        {
          Type weight = std::abs(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) : 0.
      :
      (sum1weights) ? (sum/sum1weights) : 0.;
    }