Can a Poisson distribution be Normal?
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 Normal( μ = rate*Size = λ*N, σ =√(λ*N)) approximates Poisson(λ*N = 1*100 = 100).
What’s the difference between Poisson and normal distribution?
A Poisson distribution is discrete while a normal distribution is continuous, and a Poisson random variable is always >= 0. Thus, a Kolgomorov-Smirnov test will often be able to tell the difference. When the mean of a Poisson distribution is large, it becomes similar to a normal distribution.
When does a Poisson distribution approximate a normal distribution?
As the mean of a Poisson distribution increases, the Poisson distribution approximates a normal distribution. I assume that once the Poisson mean becomes large enough, we can use normal distribution statistics.
When do you start using normal distribution statistics?
I assume that once the Poisson mean becomes large enough, we can use normal distribution statistics. Therefore we can start saying things ‘68% of the distribution will lie within 1 standard deviation of the Poisson mean’ once the mean of a Poisson distribution becomes large enough.
Why is the Poisson distribution not constant at the Student Union?
The number of students who arrive at the student union per minute will likely not follow a Poisson distribution, because the rate is not constant (low rate during class time, high rate between class times) and the arrivals of individual students are not independent (students tend to come in groups).
When did Ladislaus Bortkiewicz use the Poisson distribution?
A practical application of this distribution was made by Ladislaus Bortkiewicz in 1898 when he was given the task of investigating the number of soldiers in the Prussian army killed accidentally by horse kicks; this experiment introduced the Poisson distribution to the field of reliability engineering.