Re: fitting

*To*: mathgroup at smc.vnet.net*Subject*: [mg104761] Re: fitting*From*: Ray Koopman <koopman at sfu.ca>*Date*: Sun, 8 Nov 2009 07:26:42 -0500 (EST)*References*: <hd3mt8$9sd$1@smc.vnet.net>

On Nov 7, 3:50 am, Vadim Zaliva <kroko... at gmail.com> wrote: > Hi! > > I am very new to Mathematica and I am failing in trying to do > something very simple. > I am have the following data: > > x = {8, 36, 74, 96, 123, 152, 201, 269, 415, 460, 444, 579, 711, > 731, 602, 364, 151}; > > Which is a curve, similar to PDF function of Beta distribution: > > ListLinePlot[x] > > And I am trying to fit it to: > > PDF[BetaDistribution[\[Alpha], \[Beta]], x > > finding Alpha and Beta values. > > I will appreciate it somebody can give me a hint how to do this > properly using FindFit or any other means. I am too embarrassed > to post my modest attempts here, but trust me, I've spent few > hours trying before posting :) > > Vadim You haven't said what your 'x' represents or how it is supposed to relate to the Beta distribution. If we take the values as the counts in equal-width bins that cover [0,1], then we can get the sample mean and variance using the midpoints of the bins as the x-values, and use the method of moments to estimate 'a' and 'b', the parameters of the distribution. k = Length[f = {8, 36, 74, 96, 123, 152, 201, 269, 415, 460, 444, 579, 711, 731, 602, 364, 151}] x = Range[1/2,k]/k; {n = Tr@f, N[m = f.x/n], N[v = f.x^2/n - m^2]} Solve[{m == a/(a+b), v == m(1-m)/(1+a+b)}, {a,b}]//Flatten//N 17 {5416, 0.653065, 0.0391941} {a -> 3.12214, b -> 1.65861}