numberOfParameters

How many parameters the estimator actually estimated from the data.

This is the estimator's own count rather than the size of the distribution type's declared parameter set, and the two can differ. A distribution type has a fixed parameter schema, so a family whose members vary in how many parameters they fit will declare slots that a particular fit did not estimate. The metalog is the case in the library: boundedness is derived from the bound values rather than being part of the type, so every metalog type declares both bounds, and an unbounded fit estimated two fewer parameters than the schema lists.

This count is the one goodness-of-fit tests need, since it is subtracted from the degrees of freedom. It is not what the information criteria use: the AIC and BIC scoring models take their parameter count from the distribution itself, so changing this does not affect any score or ranking.

One imprecision remains. An estimator that is handed a parameter rather than estimating it still declares a name for it, so a metalog fitted with a supplied bound counts that bound.