Le Cam's theorem
From Infogalactic: the planetary knowledge core
In probability theory, Le Cam's theorem, named after Lucien le Cam (1924 – 2000), states the following.
Suppose:
- X1, ..., Xn are independent random variables, each with a Bernoulli distribution (i.e., equal to either 0 or 1), not necessarily identically distributed.
- Pr(Xi = 1) = pi for i = 1, 2, 3, ...
- (i.e. follows a Poisson binomial distribution)
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.
References
- Lua error in package.lua at line 80: module 'strict' not found.
- Lua error in package.lua at line 80: module 'strict' not found.
- Lua error in package.lua at line 80: module 'strict' not found.