Re: Gamma Distribution Question


"Anon." <bob.ohara@xxxxxxxxxxx> wrote in message news:TF9yi.210092$3y6.32639@xxxxxxxxxxxxxxxxxxxxxxxxxxxxx
Have you tried looking at a Poisson? You have discrete counts, so a Poisson distribution would be a better start.

Yes, I looked at Poisson. It does not fit Poisson at all. The sample mean is 26.4 and the sample variance is 129.8. On the histogram, a Poisson distribution gives a narrow lump that does not fit the data at all.


On causative mechanisms: if the rate at which organs are used is constant, then you expect the number of organs used in a set time interval to follow a Poisson distribution. The waiting time between organs being used will follow an exponential distribution.

It's more complex. The rate at which donors appear is constant (more or less); however, a given donor will yield 0-7 organs. The distribution of organs per donor does not follow a Poisson distribution either. I've uploaded that graph here:

http://www.mixedasians.com/member_pics/haplotype_1187589158.gif

Organs per donor are affected by factors such as the donor's age or cause of death. These vary in complex ways throughout the year; the marginal distribution is essentially nonparametric.


Often there is more variation than the Poisson predicts. One way of modelling that is to assume that the rate varies between time periods, and that the rate is drawn randomly from a gamma distribution (I don't know a mechanistic explanation for why a gamma is appropriate, but it's convenient mathematically). In this case, the counts follow a negative binomial distribution.

I hear what you're saying. In the organ donation business however, each organ has differing requirements, again affected by donor's age and cause of death. Kidneys tend to be the easiest to recover, while hearts and lungs are more fragile. Essentially, organs per donor is a sum of 7 different Bernoulli trials with differing probabilities.

.

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