I am trying to figure out the probability of at least n points for an inhomogeneous poisson point process defined on the real line.
$$ P\{N(a,\infty) \ge n \} = ? $$
I'm also not entirely sure if the following is valid (ie. integrating up to infinity):
$$ P\{N(a,\infty) = n \} = \frac{[\Lambda(a,\infty)]^n}{n!}e^{-\Lambda(a,\infty)} $$
where $\lambda(t)$ is some locally integrable positive function (for t>0)
$$ \Lambda(a,\infty) = \int_{a}^{\infty}\lambda(t)dt $$