The Statistics menu option computes the quantile values for all selected field quantities and a user-specified probability value. For each selected quantity, a single result object is created. Each result object is a field vector containing the quantile at each mesh position.
Note: Quantiles need to have at least 20 input samples.
Given a cumulative distribution function F(Y), the quantile
value q for a specific probability p
is defined as:
where Y denotes the quantity and k
denotes the mesh position.
The CDF is approximated from the given sample values. Generally, oSP3D uses the
CDF of a histogram. At its "tails" (for small and large probabilities), oSP3D
approximates the CDF by a quadratic regression model for an assumed Gaussian
distribution. This strategy ensures that quantile values beyond the actual value
bounds min[Yk] and
max[Yk] can be
obtained.
Usage
Compute the quantile value of
pif you are interested in the value that is not exceeded by the probabilityp.Compute the quantile value of
1−pif you are interested in the value that is exceeded by the probabilityp.Typical quantile probabilities are 0.135% (
p=0.00135) and 99.865% (p=0.99865).