num
The number of free parameters of the fitted mixture, as an information criterion should charge them: one fewer than the number of components for the mixing weights, since they are constrained to sum to one, plus every estimated parameter of every component including any estimated shift.
The library's mixture distribution reports its parameters as the mixing cumulative distribution followed by the component parameters, which counts as many weights as there are components. Reading the parameter count from that array therefore overstates the dimension by one, so the criteria in this package are supplied this value explicitly rather than reading it from the assembled distribution.