Estimating a Poisson intensity λ using classical statistics
In many problems involving a Poisson process, we need to determine a Poisson rate or intensity (e.g. expected number of car crashes in a year, or concentration of particles suspended in a liquid). To do so, you will have had some observations a in a certain amount of exposure t. For example:
α = counted particles t = amount of liquid looked at
α = car crashes t = amount of time in which crashes occurred
α = typing errors t = amount of text reviewed
This section describes three methods:
The crudest method, not recommended, but explained so you know why to avoid it.
Commonly used. It offers some improvement over the Poisson distribution method, but still cannot be applied when a = 0, and gives incorrect results at extremes.
The best method that works for all values of a and t. It is also closely aligned to Bayesian results.