GeneralStatistics(3)               QuantLib               GeneralStatistics(3)

       GeneralStatistics - Statistics tool.

       #include <ql/math/statistics/generalstatistics.hpp>

   Public Types
       typedef Real value_type

   Public Member Functions

           Size samples () const
               number of samples collected
           const std::vector< std::pair< Real, Real > > & data () const
               collected data
           Real weightSum () const
               sum of data weights
           Real mean () const
           Real variance () const
           Real standardDeviation () const
           Real errorEstimate () const
           Real skewness () const
           Real kurtosis () const
           Real min () const
           Real max () const
           template<class Func , class Predicate > std::pair< Real, Size >
               expectationValue (const Func &f, const Predicate &inRange)
           Real percentile (Real y) const
           Real topPercentile (Real y) const


           void add (Real value, Real weight=1.0)
               adds a datum to the set, possibly with a weight
           template<class DataIterator > void addSequence (DataIterator begin,
               DataIterator end)
               adds a sequence of data to the set, with default weight
           template<class DataIterator , class WeightIterator > void
               addSequence (DataIterator begin, DataIterator end,
               WeightIterator wbegin)
               adds a sequence of data to the set, each with its weight
           void reset ()
               resets the data to a null set
           void reserve (Size n) const
               informs the internal storage of a planned increase in size
           void sort () const
               sort the data set in increasing order

Detailed Description
       Statistics tool.

       This class accumulates a set of data and returns their statistics (e.g:
       mean, variance, skewness, kurtosis, error estimation, percentile, etc.)
       based on the empirical distribution (no gaussian assumption)

       It doesn't suffer the numerical instability problem of
       IncrementalStatistics. The downside is that it stores all samples, thus
       increasing the memory requirements.

Member Function Documentation
   Real mean () const                     angle = ac{ w_i x_i}{ w_i}. ]
       returns the mean, angle.d]as gle x
   Real variaight)^2const
       anglens the variance, defined as ma^2 = ac{N}{N-1} tgle t( x-gle x

   Real standardDeviation () const
       returns the standard deviation $ ma $, defined as the square root of
       the variance.

   Real errorEstimate () const
       returns the error estimate on the mean value, defined as $ \psilon =
       ma/t{N}. $        angle}{ma^3}. ] The above evaluates to 0 for a
   Real skewnight)^3const
       anglens the skewness, defined as ac{N^2}{(N-1)(N-2)} ac{tgle t( x-gle x

       Gaussian distribution.              angle}{ma^4} -
   Real kurtosis () const      ight)^4
       returns the excessangleosis, defined as ac{N^2(N+1)}{(N-1)(N-2)(N-3)}
       ac{tgle t(x-gle x
       ac{3(N-1)^2}{(N-2)(N-3)}. ] The above evaluates to 0 for a Gaussian

   Real min () const
       returns the minimum sample value

   Real max () const
       returns the maximum sample value

   std::pair<Real,Size> expectationValue (const Func & f, const Predicate &
       inRange) const
       Expectation value of a functiight]f=$ac{_{xgivin thcal{R}}hf(x{i) w,i}{
       i.e., thrm{E}t[f ;|; thcal{R}                                 r
       _{x_i in thcal{R}} w_i}. ] The range is passed as a boolean fu{ction
       returning true if the argument belongs to the range or false oxherwise.
                                                   r                 }
       The function returns a pair made of the resu{t and the number }f
       observations in the given range.            x                 w
                                                   }                 _   r
   Real percentile (Real y) const                  $                 i   {
       $ y $-th percentile, defined as the value $ st y = ac{_{x_i < }   x
                                                   u   r             {   }
       Precondition:                               c   {             _   }
           $ y $ must be in the range $ (0-1]. $   h   x             i   w
                                                   t   }             w   _
   Real topPercentile (Real y) const               h   $             _   i
       $ y $-th top percentile, defined as the value $ st y = ac{_{x_i > }
                                                       u             }   {
       Precondition:                                   c             ]   _
           $ y $ must be in the range $ (0-1]. $       h                 i
                                                       t                 w
   void add (Real value, Real weight = 1.0)            h                 _
       adds a datum to the set, possibly with a weight                   i
       Precondition:                                                     ]
           weights must be positive or null

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Version 1.10.1                  Wed Feb 7 2018            GeneralStatistics(3)