Le Cam's theorem
In probability theory, Le Cam's theorem, named after Lucien Le Cam, states the following.
Suppose:
Then
In other words, the sum has approximately a Poisson distribution and the above inequality bounds the approximation error in terms of the total variation distance.
By setting pi = λn/n, we see that this generalizes the usual Poisson limit theorem.
When is large a better bound is possible:
It is also possible to weaken the independence requirement.
