Truncate

Function Truncate

Returns a distribution with the shape of uncertain quantity ux, truncated so that it has no values below xmin or above xmax.

Declaration

Truncate(ux: numeric sample; xmin, xmax: optional scalar)

Details

When evaluated in Mid mode, it returns an estimate of the median of the truncated distribution. It always evaluates ux probabilistically and xmin and xmax according to context. The function must be given either xmin or xmax or both: Otherwise, it will give an evaluation error.

When evaluated in Sample mode, the a re-sampling algorithm obtains sampleSize sample points between the bounds using an estimated shape of the original distribution (where the estimated shape is based on the original distribution's sample). This can be applied to any continuous distribution.

Special Cases

If all values of ux <= xmin, it returns a sample = xmin. Similarly, if all values of ux >= xmax, it returns a sample = xmax.

It flags an evaluation error if xmin > xmax.

Truncate() "semi-preserves" the rank-order of sample ux: Given Y = Truncate(X, xmin), then X[Run=i] < X[Run=j] ==> Y[Run=i] <= Y[Run=j]. Hence, if all values of X are unique, the ranks are preserved -- i.e. the ranks of sample Y will correspond to the ranks of sample X. If X contains some repeated values, the ranks may not be all preserved.

Possible Future Enhancement

An optional flag might be added to return Max([xmin,Min([xmax,Mid(ux)])]) in Mid mode, rather than an estimate of the median. The median is the "correct" value according to Mid semantics, but has the disadvantage of requiring the original distribution to be evaluated in sample mode. In some large sampling applications, where explicit loops are programmed to avoid evaluating full samples in memory, this ability to avoid a full sample may offset (in some cases) the error from the approximation.