Inter-arrival time distribution for the non-homogeneous Poisson process
  We derive an analytical expression of the inter-arrival time distribution for a non-homogeneous Poisson process (NHPP). This expression is exact and is applicable to any time interval, finite or infinite. As an illustration, we present simulation results for three different intensity functions. 
Gleb Yakovlev, John B. Rundle, Robert Shcherbakov, and Donald L.   Turcotte