Plotting a probability mass function for a poisson distribution

Question

uppose that i have a poisson distribution with mean of 6 i would like to plot a probability mass function which includes an overlay of the approximating normal density.

This is what i have tried

 plot( dpois( x=0:10, lambda=6 ))

this produces

which is wrong since it doesnt contain an overlay of approxiamating noral density

How do i go about this?

Answer 1

Something like what you seem to be asking for (I'm outlining the commands and the basic ideas, but checking the help on the functions and trying should fill in the remaining details):

1. taking a wider range of x-values (out to at least 13 or so) and use xlim to extend the plot slightly into the negatives (maybe to -1.5) and

2. plotting the pmf of the Poisson with solid dots (similar to your command but with pch=16 as an argument to plot) with a suitable color, then

3. call points with the same x and y arguments as above and have type=h and lty=3 to get vertical dotted lines (to give a clear impression of the relative heights, somewhat akin to the appearance of a Cleveland dot-chart); I'd use the same colour as the dots or a slightly lighter/greyer version of the dot-colour

4. use curve to draw the normal curve with the same mean and standard deviation as the Poisson with mean 6 (see details at the Wikipedia page for the Poisson which gives the mean and variance), but across the wider range we plotted; I'd use a slightly contrasting colour for that.

5. I'd draw a light x-axis in (e.g. using abline with the h argument)

Putting all those suggestions together:

(However, while it's what you're asking for it's not strictly a suitable way to compare discrete and continuous variables since density and pmf are not on the same scale, since density is not probability -- the "right" comparison between a Poisson and an approximating normal would be on the scale of the cdfs so you compare like with like -- they'd both be on the scale of probabilities then)