Re: weibull plot on weibull scaled paper

*To*: mathgroup at smc.vnet.net*Subject*: [mg116626] Re: weibull plot on weibull scaled paper*From*: Bill Rowe <readnews at sbcglobal.net>*Date*: Tue, 22 Feb 2011 04:42:21 -0500 (EST)

On 2/21/11 at 4:19 AM, btreat1 at austin.rr.com (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.