I’m using 0−p=∞ and using the cheaty convention that e.g. 3⋅∞>2⋅∞. I think this is what you get if you regard a discrete distribution as a limit of continuous ones. If this is too cheaty, of course it’s fine just to stick with non-negative values of p.
Yeah, OK. It works but you need to make sure to take the limit in a particular way, e.g. convolution with a sequence of approximations to the identity. Also you need to assume that p>−1 since otherwise the statistic diverges even for the continuous distributions.
I’m using 0−p=∞ and using the cheaty convention that e.g. 3⋅∞>2⋅∞. I think this is what you get if you regard a discrete distribution as a limit of continuous ones. If this is too cheaty, of course it’s fine just to stick with non-negative values of p.
Yeah, OK. It works but you need to make sure to take the limit in a particular way, e.g. convolution with a sequence of approximations to the identity. Also you need to assume that p>−1 since otherwise the statistic diverges even for the continuous distributions.