In GAMLSS sigma is generally a scale parameter,
but not usually the standard deviation.
If you want the z-score for any distribution,
then it is given by:
first find the probability p of being below ...
Selecting the best model can be
(i) by choosing the fitted model with lowest generalized Akaike information criterion GAIC(k) for a user chosen penalty k for each effective degree of freedom in the ...
qBCCGo is exact, so use that.
[Note the formula for LLN is approximate and
log(1-1.645 * nu * sigma) will be NA, if 1 < 1.645 * nu * sigma.]
for calculating the ULN we need to use