Gamma - find peak

**btg202** · 07-11-2013, 07:42 AM

Hi,

I'm after finding out if anyone knows how to find the peak value of a gamma distribution. As you will know the gamma value at 0.5 probability if positively skewed will be higher than the peak point of a curve.

I'm trying to figure out how to quantitatively represent the peak value, or most likely value of the distribution.

Thanks in advance.

**martindwilson** · 07-11-2013, 08:45 AM

As you will know the gamma value at 0.5 probability if positively skewed will be higher than the peak point of a curve

wanna bet?
however maybe
http://www.youtube.com/watch?v=SAMTXAAKeug

**MrShorty** · 07-11-2013, 09:24 AM

I don't use the gamma distribution myself. But, as with almost any function, one of the things I expect you learned in calculus is that finding the maximum (or minimum) of a function is the same thing as finding the root(s) of the 1st derivative. For something like the gamma distribution, though, it is hard enough to find the expression for the function, let alone trying to find an expression for the 1st derivative. If I were programming this for myself, I'd probably use numerical derivatives.

I'm assuming you are aware of the gamma.dist function (shown a little in martindwilson's link). http://office.microsoft.com/en-us/ma...714.aspx?CTT=1 IMO, the easiest way (in Excel) to find the max of something like the gamma distribution will be to use the built in Solver utility. Set up a spreadsheet to calculate G(x) at a given alpha and beta and some "guess" at x (0.5 seems like a good first guess). Then call Solver and tell it to "set target cell" G(x) "to a maximum" "by changing" x.