# Simulate an arrival time - Cox Process?

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?

• Could you modify the math parts by using MathJax? – user158565 Nov 17 '18 at 21:33
• Apologies have not used – James65 Nov 18 '18 at 16:05