I am trying to fit the Poisson distribution to my data which is the inter-arrival times. The format of the data is:
time, count
2,3
5,1
8,2
,which means I had 3 objects with the inter-arrival time of 2 seconds, 1 object with 5 sec inter-arrival time, and so on. I a bit confused that I shall fit the Exponential distribution or Poisson distribution to these data as Poisson models the counts and Exponentials models the time between inter-arrival times.
I am using R and I am using fitdistrplus library. So, I change the data as follows
2
2
2
5
8
8
and then fit these data with fitdistrplus.
It seems that my approach agrees with :
How do you fit a Poisson distribution to table data?
But just want to be sure that I need to fit my data with Exponential distribution not with Poisson.
Best Answer
The Poisson distribution is for event counts in a given interval of time (in a Poisson process). It is not useful for modelling inter-event times.
If the events follow a Poisson process, the inter-event times will be distributed as exponential.
The usual (ML, MoM) estimator of the exponential mean is the sample mean; the ML estimator of the rate (the reciprocal of the population mean) is the reciprocal of the sample mean.