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    <p>The mean is A*B. So can you solve for perhaps A in terms of the mean(mu) and B?</p> <pre><code>A = mu/B </code></pre> <p>Of course, this does no good unless you knew B. Or does it?</p> <p>Look at your first expression. Can you substitute?</p> <pre><code>gamcdf(2.11, mu/B, B) - gamcdf(1.61, mu/B, B) = 0.90 </code></pre> <p>Does this get you any closer? Perhaps. There will be no useful symbolic solution available, except in terms of the incomplete gamma function itself. How do you solve a single equation numerically in one unknown in matlab? Use fzero.</p> <p>Of course, fzero looks for a zero value. But by subtracting 0.90, that is resolved.</p> <p>Can we define a function that fzero can use? Use a function handle.</p> <pre><code>&gt;&gt; mu = 1.86; &gt;&gt; gamfun = @(B) gamcdf(2.11, mu/B, B) - gamcdf(1.61, mu/B, B) - 0.90; </code></pre> <p>So try it. Before we do that, I always recommend plotting things.</p> <pre><code>&gt;&gt; ezplot(gamfun) </code></pre> <p>Hmm. That plot suggests that it might be difficult to find a zero of your function. If you do try it, you will find that good starting values for fzero are necessary here.</p> <p>Sorry about my first try. Better starting values for fzero, plus some more plotting does give a gamma distribution that yields the desired shape.</p> <pre><code>&gt;&gt; B = fzero(gamfun,[.0000001,.1]) B = 0.0124760672290871 &gt;&gt; A = mu/B A = 149.085442218805 &gt;&gt; ezplot(@(x) gampdf(x,A,B)) </code></pre> <p>In fact this is a very "normal", i.e, Gaussian, looking curve.</p>
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    1. COThat's terrific, thanks for the detailed answer. The fzero function is great! I'm a little bit dismayed that there's no solution, though, since the author of a paper I'm trying to reproduce said he used a distribution with exactly these characteristics as a prior distribution for an MCMC simulation. I don't suppose you're familiar with MCMC, are you? If you are, would you mind taking a quick look at page 11 of this paper and letting me know if I've misunderstood something? Here's the URL for the paper: http://bit.ly/9uWlLN .
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    2. COThe prior I gave the details for above is the first one in the chart, tau.
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    3. COI read through the paper, and then did some more playing. I needed to use better starting values for fzero, plus an interval that brackets the solution to gain convergence.
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