If I simulate arrival times using a Poisson process where the input to the Poisson process is also a Poisson process.
Input arrival rate = L , and then U1 and U2 are random draws from a uniform distribution
Simulated arrival rate = 1/ (-LN(U2)/L) =f , Arrival time = -LN(U1)/f , So then: Arrival time = -LN(U1)*(-LN(U2)/L)
This has quite nice feature that still only one input L and arrival time average will be 1/L but the arrival times will have more dispersion than a Poisson simulated arrival time.
Question: Is this a Cox process?