I'd like to automatically detect whether data have a very strongly discernable peak, with any particular distribution. The data can otherwise be quite noisy, or there might be several 'false' peaks. Here are a few examples of the performance I'd expect in a good measure, such that higher is better:
Multimodal: measure scores low
Flat: measure scores low
Jagged with no real high point: measure scores low
A well-defined peak, regardless of tail thickness or other considerations: measure scores high
Could Density Peak Clustering be a solution, particularly HDBSCAN? Or is there another clustering algorithm that's computationally faster if dedicated to finding a single peak of values?
I've also thought that this might be more of a pattern recognition problem, potentially making a neural network useful.