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Re: weibull plot on weibull scaled paper

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  • Subject: [mg116626] Re: weibull plot on weibull scaled paper
  • From: Bill Rowe <readnews at>
  • Date: Tue, 22 Feb 2011 04:42:21 -0500 (EST)

On 2/21/11 at 4:19 AM, btreat1 at (DrMajorBob) wrote:

>ProbabilityScalePlot often throws a FindRoot::jsing error with
>random data, and I wonder why.

Hmm... I've never seen this error when using ProbabilityScalePlot

>I'm also trying to see the relationship between these two graphs:

>dist = WeibullDistribution[7, 200];
>Quiet@ProbabilityScalePlot[data, "Weibull"]
>QuantilePlot[data, dist]

I assume after the second line you posted above there was
something like

data = RandomReal[dist, {100}];

else data is undefined and there would be an error when you use
either ProbabilityScalePlot or QuantilePlot. But to answer your question:

For ProbabilityScalePlot, the y-axis is the cumulative
probability function. In effect, the resulting plot is
equivalent to something like making a log-log plot of the hazard
function (HazardFunction[WeibullDistribution[7,200],t]) combined
with a log-log plot of the empirical hazard function and
modifying the y-axis to be a probability scale.

For QuantilePlot you are comparing empirical quantiles with
quantiles of the given distribution. Basically, this is a
parametric plot with the y-axis given by
Quantile[WeibullDistribution[7,200],p] and the x-axis given by
Quantile[data, p] for p running from approximately 1/n to
approximately n/(n+1) where n is the number of data points.

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