- If X ∼Poisson (λ)
⇒ X ≈N ( μ=λ, σ=√λ), for λ>20,
and approximation improves as (the rate) λ
- Poisson(100) distribution can
be thought of as the sum of 100
independent Poisson(1) variables
and hence may be
considered approximately Normal, by the central limit theorem, so
= λ*N, σ =√λ) approximates Poisson(λ*N = 1*100 = 100).
- The normal distribution is in the core of the space of all
observable processes. This distributions often provides a reasonable
approximation to variety of data. The Central Limit Theorem states that
to the distribution of the sample average (for almost any process, even
non-Normal) is normally distributed (provided the process has well
defined mean and variance).
- This applet draws random samples from Poisson distribution,
its histogram (in blue) and shows the
corresponding Normal approximation (in red).
You can specify
the rate (λ) of the
distribution and the number of trials (N)
in the dialog boxes. By changing these parameters, the shape and
of the distribution changes. This Applet gives you an opportunity to
how the approximation to the normal distribution changes when you alter
parameters of the distribution.
Last modified on
Ivo D. Dinov,
Ph.D., Departments of Statistics and Neurology, UCLA School of Medicine