Re: Measuring Time to Convergence

Inman Harvey wrote:

Generally one can expect the distribution to be something very much like a Poisson Distribution -- which has the property that the Variance equals the Mean. So yes indeed you should expect the wide variances that you are reporting. There is a close relationship between Poisson Distributions and Binomial Distributions for large sample sizes. 

.....

Look up statistics related to Poisson Distributions. Because of the high variance, any Mean that you take from a series of runs is highly noisy. There are ways of getting confidence intervals, try Googling for "Poisson distribution confidence intervals".

Inman Harvey

Thanks Inman. I actually thought of Poisson a couple of days ago, but dismissed it. I've just gone back to my textbooks. Even assuming a constant probability for each generation, I can't make it fit. I could class "not found" as an event, but then I stop as soon as no event is found.

So I suspect the operative words in your answer are "something very much like a"! And that makes sense - the shape is going to be similar with a minimum of 1 and an large positive tale that goes off to infinity.

Incidentally, using the standard sample mean and standard deviations; I'm finding my standard deviation is more than my mean. An overnight run gives standard deviations of 8-10x the mean (higher multiplier for smaller populations).

Another possibility is to create a log histogram and find the mode. Unfortunately that would requires a lot of tests.



--
Richard Marsden
Winwaed Software Technology, http://www.winwaed.com
http://www.mapping-tools.com for MapPoint tools and add-ins
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