Mixture Data Description
Everything known about a sample before a mixture is fitted to it.
The order matters. An analyst is best served by learning that their sample cannot support six components before being shown a fit at six components, and by learning that the humps they counted move with the bin width before being asked to defend the count. Both facts are cheap; neither is available from the fit.
Adequacy is deliberately absent. The plan expected the data-adequacy verdict to join this object, and it cannot: adequacy is governed by how far the fitted mixture sits from the nearest mixture with one component fewer, so it requires a fit that by definition does not exist yet. It lives on the results instead. What belongs here is the structural ceiling — the largest number of components this sample can support at all — which is available before fitting and answers the same question in the cases where the answer is emphatic.
Parameters
how many observations there are
how many of them are distinct, which is what actually limits the partition
the sample statistics
the largest number of components the sample can structurally support, from the admissibility certificate
what the mode structure looks like and whether it survives smoothing