In addition to what you say, I would also guess that e−λ∗t is a reasonable guess for P(no events in time t) when t > T, if it’s reasonable to assume that events are Poisson-distributed. (but again, open to pushback here :)
My intuition is that it’s not a great approximation in those cases, similar to how in regular Laplace the empirical approximation is not great when you have eg N<5
Id need to run some calculations to confirm that intuition though.
Thanks for the confirmation!
In addition to what you say, I would also guess that e−λ∗t is a reasonable guess for P(no events in time t) when t > T, if it’s reasonable to assume that events are Poisson-distributed. (but again, open to pushback here :)
What’s r?
Oops, I meant lambda! edited :)
I still don’t understand—did you mean “when T/t is close to zero”?
Oops yes, sorry!
My intuition is that it’s not a great approximation in those cases, similar to how in regular Laplace the empirical approximation is not great when you have eg N<5
Id need to run some calculations to confirm that intuition though.