Probability of exceeding a threshold/cutoff

The Probability from Conditional Expectation is designed to calculate the probability for a variable to be above a given threshold/cutoff at a given point using a normal score transformation of the variable and its kriging (conditional expectation).

The probability for Z to exceed a given threshold z_c is given by integrating the gaussian density function for each value greater than the gaussian anamorphosis of the threshold:

where G is the c.d.f. for the gaussian distribution.

Note: At a conditioning point, the probability is equal to 0 or 1 depending upon whether Y_ɑ is smaller or larger than φ^-1(z_c). Conversely, far from any conditioning data, the probability converges towards the a priori probability 1 - G(φ^-1(z_c)).

The Accumulation above threshold is obtained by computing the mean-expectation of the raw value for each value greater than the gaussian threshold. In multivariate, the indicator can be on another variable than the back-anamorphosis one when using the threshold on the main variable option. The final value is multiplied by the cell size to derive the volume/area accumulation

The Mean above threshold is simply derived from the previous variables by dividing the accumulation by the probability.