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boost::accumulators::impl::immediate_rolling_variance_impl — Iterative calculation of the rolling variance.
// In header: <boost/accumulators/statistics/rolling_variance.hpp> template<typename Sample> struct immediate_rolling_variance_impl : public { // types typedef ; // construct/copy/destruct template<typename Args> (); // public member functions template<typename Args> (); template<typename Args> () ; template<typename Archive> (, ); // private member functions template<typename T> (, = ); template<typename T> (, = ); };
Iterative calculation of sample variance is done as follows, see also http://en.wikipedia.org/wiki/Algorithms_for_calculating_variance. For a rolling window of size
, for the first
samples, the variance is computed according to the formula
where the sum of squares can be recursively computed as:
and the estimate of the sample mean as:
For further samples, when the rolling window is fully filled with data, one has to take into account that the oldest sample is dropped from the window. The sample variance over the window now becomes:
where the sum of squares now equals:
and the estimated mean is:
Note that the sample variance is not defined for .