[R] Fitting inter-arrival time data
azzalini at stat.unipd.it
Tue Jul 1 10:04:01 CEST 2003
On Tuesday 01 July 2003 05:16, M. Edward Borasky wrote:
> Unfortunately, the data are *non-negative*, not strictly positive. Zero is
> a valid and frequent inter-arrival time. It is, IIRC, the most likely value
> of a (negative) exponential distribution.
Not really. Zero+ is the value with highest density in a (negative) exponential
distribution, which implies that you should have *no* observed zero's from that
If you have a non-negligible fraction of 0 values, then your data are reasonably
described as having a mixed distribution:
(1) a discrete component at 0, and
(2) a continuous positive component.
Kernel (or similar) density estimation is appropriate for the continuous component
only. Notice that the same remark applies to any procedure (parametric or
non-parametric, using mixtures, etc.) which is based on continuous components only.
It *looks* that a wise procedure is to separate out the discrete and the continuos
component of your data, and handle them separately. At the end you can "merge"
the two parts into
Y = p * 0 + (1-p) * X
where p is the proportion of 0's, and X represents the continuous component of
the random variable.
Adelchi Azzalini <azzalini at stat.unipd.it>
Dipart.Scienze Statistiche, Università di Padova, Italia
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