Plotting the pdf of a negative binomial distribution using mean and stnd deviation

#1
I have been using a negative binomial distribution to describe my data; in order to allow me to randomly sample from the parameterised distributions. I have had no problems getting r (the number of successes) and p (the probability of success) for my distribution. My problem is that I would like to compare my pdf to results from a much older paper, wherein the negative binomial distribution was described in relation to it's mean and standard deviation (sd).
I use both minitab and spss and am curious as to how I plot the negative binomial pdf based on these two parameters (mean and sd). Everywhere I have looked only describes this distribution in terms of its r and p parameters.
 

BGM

TS Contributor
#2
Re: Plotting the pdf of a negative binomial distribution using mean and stnd deviatio

Simply express the parameters \( r, p \) in terms of the given mean and sd -
i.e. solving a 2x2 system of non-linear equations.
 
#3
Re: Plotting the pdf of a negative binomial distribution using mean and stnd deviatio

I'm afraid my maths background isn't great....what exactly do you mean by express the parameters in terms of the sd and mean?
 

BGM

TS Contributor
#4
Re: Plotting the pdf of a negative binomial distribution using mean and stnd deviatio

Suppose the random variable \( X \sim \text{NegBin}(r, p) \) which use the following parametrization:

http://en.wikipedia.org/wiki/Negative_binomial_distribution

then we have

\( E[X] = \frac {pr} {1 - p}, SD[X] = \frac {\sqrt{pr}} {1 - p} \)

As \( E[X], SD[X] \) are given constants, we have a system of non-linear equations in \( r, p \) which we can solve.