3 parameter distributions. pdfs?

#1
Hi, this is my first post and this looks like the most appropriate place for it. I've used minitab to get the most appropriate distributions for various sets of data. This data is then to be used to fuel inputs for a supply chain simulation model. Rather than look at the specifics of what came out I want to use the parameter estimates that come with it for the respective pdfs' and get plots so i can compare and contrast them visually.

Anyway, thats the problem area. Specifically, 3-parameter distributions keep cropping up. I cannot seem to find the pdfs for the 3-parameter gamma and 3parameter log logistic distributions. Im also wondering, if im just looking at shape, does it matter? Because the third parameter generally seems to just be a location parameter and so will just cause the curve to "shift" up and down. Am I right in assuming that. Any info would be great.

Ivor.
 

BioStatMatt

TS Contributor
#3
In the Gaussian (Normal) PDF, there are two parameters, one for location (mean) and one for scale (variance). The gamma distribution also has two parameters, however, they do not have the same meaning as that for the normal. The mean and variance of the gamma are both functions of the two parameters. Hence, It is not possible to say which parameter has a greater effect of the location or scale of the distribution.

As for your problem, I imagine that you are giving Minitab a set of data and it tells you what distribution provides the best fit and estimates of its parameters. In this case, it has suggested the generalized gamma, which has three parameters. This probably means that the two parameter gamma (and other two parameter distributions) were insufficient to capture the variation in the empirical distribution (your data). Given this, perhaps you should stick with the three parameter gamma.

For plotting the PDF, you could use the function that is displayed at the HTML address given by mp83. However, you should make sure that the parameters in this function corrospond to those given by Minitab, as there are several parametrizations of the gamma PDF.

~Matt