Interarrival time
Topic of Poisson processes, part of Stochastic processes
Interarrival time
| Type | Topic |
| Taught in | Poisson processes |
| Part | Stochastic processes |
The wait W_n=T_n-T_{n-1} between successive events of a counting process. For a homogeneous Poisson process of rate \lambda the interarrival times are independent exponentials with mean 1/\lambda, and the arrival times T_n are their partial sums; the converse construction gives a Poisson process too.
In Poisson processes
From Poisson processes
T_1 is exponential with rate \lambda, in the parameterisation on the distribution sheet: density \lambda e^{-\lambda t} on (0,\infty), mean 1/\lambda. Independent increments make the later interarrival times W_1,W_2,\ldots independent copies of that exponential law. The arrival times are the partial sums T_n=\sum_{i=1}^n W_i. The construction runs in reverse as well. Independent exponential interarrival times of rate \lambda produce a Poisson process of rate \lambda.
Used in
See also
Event · Homogeneous Poisson process · Forward equations of the Poisson process · Nonhomogeneous Poisson process · Superposition and thinning · Spatial Poisson process · Intensity function