With Respect
The most helpful general references I got were to Wikipedia(starting from http://en.wikipedia.org/wiki/Gamma-distribution) and to N.L. Johnson and Samuel Kotz Continuous Univariate Distributions.
I thought my ratio of rwo variables approximated to the shape of one exponential distribution, a special case of gamma.But trying to estimate parameters has shown me that if it is a gamma distribution I have it is one with k<1; the shape is more like the exponential than any of the higher-k gammas, but differs from it in the way opposite to them.
Three-parameter gamma is referred to in message 017726 on this list(05/12/05)
I have used StatsDirect to create a random-numbers gamma distribution with the parameters I calculated from my data.I have compared the two both with a Smirnov test, whose results I was unsure how to interpret, and by plotting points with one as x-axis and the other as y-axis, which gave me almost a straight diagonal line (with small kinks).
Yours Sincerely,
Alan E. Dunne
> I will answer part of your question.
> For me a typical Gamma dist is one whose density initially increases and then
> decreases. I am not sure if when you talk about three parameter gamma,
> you mean
> the variant with a shift (i.e. instead of (0,infinity) look at (a, infinity)
> and "a" is the third parameter in this case but it obviously does not change
> the shape of the didtribution.
>
> To test if the distribution of your data is a gamma (or any other
> distribution)
> , use probability plots (there ar evariants called QQ plots or similar).
> Most statistical software provide these. Menu driven software also
> will let you
> specify the distribution (gamma in your case) and may be the parameters.
> Roughly speaking, if the plot "resembles" a straight line, than you are
> spot on.
> These plots are usually accompanied by p-values or similar statistics so that
> you may use also a traditional statistical judgement.
> Most of the statistics should be interpreted cautiously if the
> parameters of the
> distribution are estimated from the data (rather than supplied by you) but
> otherwise I have found them very useful for the task.
>
> You don't mention particular books but probably the volumes of Johnson
> and Kotz
> are the best place for initial reference.
>
> Best regards,
> Georgi Boshnakov
>
> ============================
> Georgi Boshnakov
> School of Mathematics
> University of Manchester
> Manchester M60 1QD
> UK
Alan,
I saw your allstat posting. I find www.xycoon.com a useful resource for density function and other formulae relating to statistical distributions with which I am not familiar - it has a good section on continuous distributions and includes relationships among them. This may be obvious, but watch out that you don't confuse the "gamma distribution" for the "gamma function" (gamma(x) = (x-1)! where x is an integer).
Dominic Muston
Hi
For general info on distributions try wikipedia
e.g. http://en.wikipedia.org/wiki/Gamma-distribution
>> How can I test whether my dataset approximates a gamma distribution?
To test whether two datasets come from the same distribution use a Kolmogorov-Smirnov test.
If one of the datasets is your real test data, and the other is sampled from the gamma distribution, then you have your test.
K-S tests come in two forms (in stata)
2 sample - your supply two datasets
1 sample - you supply your test dataset, and specify the distribution they are to be tested against.
Desmond
Respect for digging up so much literature to understand Gamma
distribution. There's a lot in your email that I don't know. But in my
diploma in Statistics, we did learn something simple which you didn't
seem to have mentioned. The Gamma distribution represents the
distribution of time until the n events if events occur with constant
rate. The Exponential distribution is thus a special case of the Gamma
as it's the distribution of time until the occurance of the first event.
The Chi-square distribution is also a special case of the Gamma.
Regards,
Tim
[Timothy Mak]
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