# [R] Fitting inter-arrival time data

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
distribution.

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.

best wishes,