# StatisticsAccumulator class

`StatisticsAccumulator`

computes population statistics by accumulating the first four central moments.

Samples are added one by one, using the `Push`

method. Other members are used to retrieve estimates of
the population statistics based on the samples seen up to that point. Formula used to compute population
statistics are corrected, though the standard deviation, skewness and excess kurtosis are not unbiased
estimators. The accumulator uses a stable algorithm to prevent catastrophic cancellation.

It is possible to accumulate samples in different objects (e.g. when processing with multiple threads),
and add the accumulators together using the `+`

operator.

## Functions

- void Reset()
- Reset the accumulator, leaving it as if newly allocated.
- void Push(dip::dfloat x)
- Add a sample to the accumulator
- auto Number() const -> dip::uint
- Number of samples
- auto Mean() const -> dip::dfloat
- Unbiased estimator of population mean
- auto Variance() const -> dip::dfloat
- Unbiased estimator of population variance
- auto StandardDeviation() const -> dip::dfloat
- Estimator of population standard deviation (it is not possible to derive an unbiased estimator)
- auto Skewness() const -> dip::dfloat
- Estimator of population skewness. This estimator is unbiased only for symmetric distributions (it is not possible to derive an unbiased estimator).
- auto ExcessKurtosis() const -> dip::dfloat
- Estimator of population excess kurtosis. This estimator is only unbiased for normally distributed data (it is not possible to derive an unbiased estimator).

## Operators

- auto operator+=(dip::StatisticsAccumulator const& b) -> dip::StatisticsAccumulator&
- Combine two accumulators