Class IncrementalStatistics

adds a datum to the set, possibly with a weight

adds a sequence of data to the set, with default weight

returns the downside deviation, defined as the square root of the downside variance.

number of negative samples collected

returns the downside variance, defined as $$ \frac{N}{N-1} \times \frac{ \sum_{i=1}^{N} \theta \times x_i^{2}}{ \sum_{i=1}^{N} w_i} $$, where $ \theta $ = 0 if x > 0 and $ \theta $ =1 if x <0

returns the error estimate $ \epsilon $, defined as the square root of the ratio of the variance to the number of samples.

returns the excess kurtosis, defined as $$ \frac{N^2(N+1)}{(N-1)(N-2)(N-3)} \frac{\left\langle \left(x-\langle x \rangle \right)^4 \right\rangle}{\sigma^4} - \frac{3(N-1)^2}{(N-2)(N-3)}. $$ The above evaluates to 0 for a Gaussian distribution.

returns the maximum sample value

returns the mean, defined as $$ \langle x \rangle = \frac{\sum w_i x_i}{\sum w_i}. $$

returns the minimum sample value

resets the data to a null set

number of samples collected

returns the skewness, defined as $$ \frac{N^2}{(N-1)(N-2)} \frac{\left\langle \left( x-\langle x \rangle \right)^3 \right\rangle}{\sigma^3}. $$ The above evaluates to 0 for a Gaussian distribution.

returns the standard deviation $ \sigma $, defined as the square root of the variance.

returns the variance, defined as $$ \frac{N}{N-1} \left\langle \left( x-\langle x \rangle \right)^2 \right\rangle. $$

sum of data weights