Re: fitting

*To*: mathgroup at smc.vnet.net*Subject*: [mg104772] Re: fitting*From*: Mark Fisher <particlefilter at gmail.com>*Date*: Mon, 9 Nov 2009 05:45:55 -0500 (EST)*References*: <hd3mt8$9sd$1@smc.vnet.net>

On Nov 7, 6:50 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 Borrowing from both Ray and Dan, I interpret the data as bin counts and use FindFit: Clear[a, b, x]; bincounts = {8, 36, 74, 96, 123, 152, 201, 269, 415, 460, 444, 579, 711, 731, 602, 364, 151}; nbins = Length[bincounts]; bincenters = Range[1/2, nbins]/nbins; binheights = Normalize[bincounts, Total[#]/nbins &]; bindata = Transpose[{bincenters, binheights}]; fit = FindFit[bindata, PDF[BetaDistribution[a, b], x], {a, b}, {x}]; dist = BetaDistribution[a, b] /. fit; Plot[PDF[dist, x], {x, 0, 1}, Epilog -> {ColorData[1][2], Point[bindata]}, PlotLabel -> Column[(fit /. Rule -> Equal)]] --Mark