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On Thu, Aug 6, 2009 at 6:02 PM, Pierre GM<pgmdevlist@gmail.com> wrote:
On Aug 6, 2009, at 5:49 PM, Robert Kern wrote:
On Thu, Aug 6, 2009 at 16:43, Pierre GM<pgmdevlist@gmail.com> wrote:
Even if the scale is simply discarded already, using a location will probably NOT give the expected result
It depends on what your expectations are. For the discrete distributions, all the loc parameter means is this, as documented:
pmf(x; loc) -> pmf(x-loc)
That's it. I don't know why you would expect anything else.
Because using a location parameter, you change the support domain. Back to the example of a Poisson distribution with loc=1, the support domain is now x>=1, which amounts to truncating the zeroes. The mean of a zero-truncated Poisson with parameter pr should be pr/(1-exp(- pr)), but we end up with pr+1. Not the expected result. I think it's a source of confusion to keep a location parameter for discrete distributions. it'd be worth to implement method to allow truncation, but just a loc parameter doesn't do it.
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loc just shifts the distribution on the real/integer line. except for the fit method (which doesn't exist for discrete distribution), I don't see any real disadvantage to having loc in there as an option, but I guess in many cases it won't be very useful either. I think there are also discrete distribution with unbound support +/- inf for which a loc shift would make sense. The big advantage of the current setup, as Robert said, is consistency, both in the implementation and in code that goes over all (or a large set of) distribution(s). But for a long time, I have been all in favor of "fixing" the fit method, and possibly introduce a semi-frozen distribution class, but for this I don't see why we should special case location. fixing loc is the main use case, but for example estimation with the scale parameter fixed is also a common use case. Josef