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Re: weibull plot on weibull scaled paper

• To: mathgroup at smc.vnet.net
• Subject: [mg116687] Re: weibull plot on weibull scaled paper
• From: Darren Glosemeyer <darreng at wolfram.com>
• Date: Thu, 24 Feb 2011 06:21:14 -0500 (EST)

On 2/23/2011 4:24 AM, Bill Rowe wrote:
> On 2/22/11 at 1:12 PM, btreat1 at austin.rr.com (DrMajorBob) wrote:
>
>> This gave the FindRoot:jsing error on the first try just now... and
>> also the third try.
>> dist = WeibullDistribution[7, 200];
>> data = RandomVariate[dist, 300];
>> ProbabilityScalePlot[data, "Weibull"]
>> QuantilePlot[data, dist]
>> So the error is not unusual.
> Hmmm... If I copy and paste just
>
> dist = WeibullDistribution[7, 200];
> data = RandomVariate[dist, 300];
> ProbabilityScalePlot[data, "Weibull"]
>
> into a single cell then execute it, I see the error you
> reported. Alternatively, if I type the above by hand into a
> single cell I still see the error you reported consistently. Or
> I can copy each line one by one pasting each into a cell then
> execute each line before pasting the next and still get the error.
>
> But if I enter each line by hand into individual cells, I don't
> see the error. So, there appears to be a bug somewhere. That is,
> the various ways I've described above of doing the computation
> should all behave identically.
>
>

ProbabilityScalePlot and its friends call the internal parameter 
estimation code for FindDistributionParameters/EstimatedDistribution to 
get the estimates. The reason for the message is that the equations in 
the estimation code for WeibullDistribution were less numerically stable 
than they could have been and so convergence fails more often than it 
should when parameter values are somewhat large. This has been fixed for 
the next release.

I think the fact that the example worked without error when you typed 
the inputs in separate cells is a red herring. The example will converge 
for some data sets and not for others. I suspect the random values you 
got in the case that worked just happened to give a convergent result 
while the random values you'd gotten in the other attempts did not.

Darren Glosemeyer
Wolfram Research