Visible to Intel only — GUID: GUID83750A145B694AB2B627F2B02E8BB455
Visible to Intel only — GUID: GUID83750A145B694AB2B627F2B02E8BB455
Estimating Raw and Central Moments and Sums, Skewness, Excess Kurtosis, Variation, and VarianceCovariance/Correlation/CrossProduct Matrix
Summary Statistics offers the following methods to support computation of raw and central moments and sums, skewness, excess kurtosis (further referred to as kurtosis), variation, and variancecovariance/correlation/crossproduct matrix:
Method VSL_SS_METHOD_FAST is a performanceoriented implementation of an algorithm for estimate calculations.
Method VSL_SS_METHOD_FAST_USER_MEAN is an implementation of an algorithm for estimate calculations when a userdefined mean is provided.
Method VSL_SS_METHOD_1PASS is an implementation of a onepass algorithm. In this case, all requested estimates are computed for a single pass. For example, see [West79].
Method VSL_SS_METHOD_CP_TO_COVCOR is an implementation of computation of a variancecovariance and/or correlation matrix from a corresponding crossproduct matrix.
Method VSL_SS_METHOD_SUM_TO_MOM is an implementation of computation of raw/central statistical moments as well as kurtosis/skewness/variation from corresponding raw/central sums.
The VSL_SS_METHOD_FAST method for variancecovariance estimation can be numerically unstable for some datasets, such as a dataset from Gaussian distribution with a standard deviation several orders smaller than its mean. For such datasets, to estimate variancecovariance, crossproduct or another estimate relying on mean, use the onepass algorithm supported by the library, or the twopass algorithm [West79], whose building blocks are available in the library. In the latter case, you need to do the following:
Compute the mean using Summary Statistics functions.
Compute the variancecovariance, crossproduct or another estimate by providing the computed mean and applying the VSL_SS_METHOD_FAST_USER_MEAN method.
Each estimate is stored as a onedimensional array. The size of the array may differ depending on the type of the estimate, as follows:
Estimate Type  Size of the Array 


Must be sufficient to store at least p elements, where p is the dimension of the task. 

Depends on the storage format. For details, see Table Storage formats of a variancecovariance/correlation/crossproduct matrix in the Summary Statistics section of [MKLMan]. 