Le Cam's theorem

In probability theory, Le Cam's theorem, named after Lucien Le Cam, states the following.

[1][2][3] 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.

is large a better bound is possible:

Pr (

represents the

min

operator.

It is also possible to weaken the independence requirement.