# [R] Weibull point process

Rolf Turner rolf.turner at xtra.co.nz
Thu Sep 15 12:12:54 CEST 2011

On 15/09/11 19:24, Torbjørn Ergon wrote:
> On Thu, 15 Sep 2011 09:47:35 +1200, Rolf Turner
> <rolf.turner at xtra.co.nz> wrote:
>> On 15/09/11 07:21, Torbjørn Ergon wrote:
>>> Dear list,
>>>
>>> I'm looking for a function to generate (simulate) a random Weibull
>>> point process. Can anyone help?
>>>
>>> Cheers,
>>>
>>> Torbjørn Ergon, University of Oslo
>>
>> Do you mean a renewal process with the inter-event times having
>> a Weibull distribution?  Should be trivial to code up, using rweibull.
>>
>>     cheers,
>>
>>         Rolf Turner
>
>
>
> Yes, in a way - but the parameters of the Weibull must change after
> each event. I'm trying to simulate events that can happen multiple
> times thru the life of an individual and where the hazard rate is age
> dependent according to a Weibull hazard. Hence, after the first event
> has occurred at time t1 the hazard rate should be h(x; t1,
> shape,scale) = (shape/scale)*((x-t1)/scale)^(shape-1). This doesn't
> seem trivial to do using 'rweibull' - but perhaps I'm missing
> something (trivial).

Unless I am terribly confused your hazard function is just the hazard
function
of a Weibull distribution ``starting off'' from t1 rather than starting
off from 0.
So a random variable having that hazard function would have the same
distribution
as t1 + X where X is Weibull with the given shape and scale.

So you can just create the points of your process as the cumulative sum of
a number of independent Weibull variates.

Perhaps I'm not seeing things correctly.  If so, would some wiser person