Calculating the Non-exceedance Probability

The Statistics menu option Quantiles and probabilities > Non-exceedance probability computes the non-exceedance probabilities for all selected field quantities and a user-specified threshold value. For each selected quantity, a single result object is created. Each result object is a field vector that contains the probability at each mesh position.

Note:  Quantiles need to have at least 20 input samples.

Given a cumulative distribution function F(Y), the probability p for a quantile value q is defined as:

where Y denotes the quantity and k denotes the mesh position.

The CDF is approximated from the given sample values as described in Calculating Quantile Values.

Usage

  • Compute the probability pk for which a certain threshold q is not exceeded.

  • If you are interested in the exceedance probability, you need to interpret the values using 1−pk.