FindFit, Weibull

*To*: mathgroup at smc.vnet.net*Subject*: [mg92868] FindFit, Weibull*From*: P_ter <petervansummeren at gmail.com>*Date*: Thu, 16 Oct 2008 05:04:48 -0400 (EDT)

I found some data which seemed to fit a WeibullDistribution. The data are: pr= {16, 34, 53, 75, 93, 120}; After adding the median rank to the data: praxis={{16, 0.109101}, {34, 0.26445}, {53, 0.421407}, {75, 0.578593}, {93, 0.73555}, {120, 0.890899}}; I checked with LeastSquares the parameters: \[Alpha]=1.4301;\[Beta] = 76.318. So far ok. But the following did not work: fit2 = {a, b} /. FindFit[praxis, CDF[WeibullDistribution[a, b], x], {a ,b}, {x}] So, I used the parameters in the Weibull CDF and the times from pr to get: praxis1= {{16, 0.106157}, {34, 0.27559}, {53, 0.451308}, {75, 0.623149}, {93, 0.73256}, {120, 0.848082}} (something went wrong with editing, so maybe I sent a by accident an unfinished message) I checked with FindFit and it worked. But then I gave extra some variations: praxis2 = {#, RandomReal[{0.95, 1.05}] CDF[WeibullDistribution[1.4, 76.318], #]} & /@ pr; fit4 = {a,b} /. FindFit[praxis2, CDF[WeibullDistribution[a,b], x], {a,b}, {x}] After a few times trying the two above lines FindFit did not work. It could be ok. But it seems to me that FindFit with a such a small relative variation in the data from 0.95 to 1.05 should still work. How can I use FindFit in the case of praxis in a safe way? Thanks in advance. P_ter

**Follow-Ups**:**Re: FindFit, Weibull***From:*Darren Glosemeyer <darreng@wolfram.com>