Re: Re: WeibullDistribution
- To: mathgroup at smc.vnet.net
- Subject: [mg42618] Re: [mg42590] Re: WeibullDistribution
- From: Dr Bob <drbob at bigfoot.com>
- Date: Fri, 18 Jul 2003 05:25:12 -0400 (EDT)
- References: <200307170745.DAA23009@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
I would think the CDF -- anchored as it is at its end-points -- would obscure things. Fitting it will make a Chi-square goodness of fit look good, but perhaps at the cost of really fitting the shape of the PDF. Bobby On Thu, 17 Jul 2003 03:45:09 -0400 (EDT), Bill Rowe <listuser at earthlink.net> wrote: > On 7/16/03 at 9:13 AM, robert.nowak at ims.co.at (Robert Nowak) wrote: > >> what about doing a NonlinearFit on the empirical CDF of the data >> against the CDF of the desired dsitribution. are there any >> tehoretical issues against such a fit ? > > Yes, you can use NolinearFit to fit the empricial CDF of the data to the > theorectical CDF. And yes, there are pros and cons. > > The primary disadvantage of using NonlinearFit is the difficulty in > finding the true least squares fit, i.e., the set of paramerters that > makes the summed square error globally minimal. It is often the case > there are several local minina and it is easy for the non-linear > algogrithm to get trapped in a local minima. And the real difficulty is > there is no simple way of determining when this happens. > > The primary advantage of using NonlinearFit is you truly are minimizing > the least squares. This is particularly important when you want > confidence limits on the fitted parameters. If you assume the usual > model, i.e., the errors are normally distributed about the regression > curve then you can use the usual normal distribution based statistics to > compute the confidence limit. In fact, this is what NonlinearRegress does > assume when it computes confidence limits. > > It is possible to correctly compute confidence limits with the > transformed problem. But this is much more difficult to do correctly. > >> of course is see that linear fitting is much more elegant but isn't >> there a danger to get som bias in the estimated parameters due to the >> transformations isn't it neccessary to weight the data properly to >> take the transformations into account ? > >> From a practical standpoint, no the linear fit to the transformed >> problem is good as is with out adjustments. Generally, the uncertainty >> in the fitted parameters is larger than the bias particularly when >> attempting to find parameters for a given distribution. Also it is very >> easy with the Weibull distribution to make point estimates based on two >> selected quantiles. These can easily be made free of bias and compared >> to the estimates from the transformed regression problem. > > -- majort at cox-internet.com Bobby R. Treat
- References:
- Re: WeibullDistribution
- From: Bill Rowe <listuser@earthlink.net>
- Re: WeibullDistribution