Poisson(lambda=x) vs Normal(mean=x, sd=sqrt(x))
Mauricio Alarcon
March 12, 2015
For any given dataset with mean=x and sd=sqrt(x), both the Poisson and Normal distributions can be good pdfs.
In this example, I’m comparing poisson and normal distributions with the following paramenters:
- Mean: 25
- Standard Deviation: 5
- Lambda: 25
Both Poisson(lambda=25) and Normal(mean=25, sd=5) are awfully similar as we can see below:
Summary
| x | Poisson(lambda=25) | Normal(mean=25, sd=5) | |
|---|---|---|---|
| Min. : 5 | Min. :0.00000 | Min. :0.00003 | |
| 1st Qu.:15 | 1st Qu.:0.00083 | 1st Qu.:0.00089 | |
| Median :25 | Median :0.00989 | Median :0.01080 | |
| Mean :25 | Mean :0.02439 | Mean :0.02439 | |
| 3rd Qu.:35 | 3rd Qu.:0.04541 | 3rd Qu.:0.04839 | |
| Max. :45 | Max. :0.07952 | Max. :0.07979 |
Histograms
Question
If I have a dataset and find that sd=sqrt(mean), what’s the criteria for favoring one distribution vs the other?