Re: Plotting a simple line at a weibull

*To*: mathgroup at smc.vnet.net*Subject*: [mg125330] Re: Plotting a simple line at a weibull*From*: Bill Rowe <readnews at sbcglobal.net>*Date*: Wed, 7 Mar 2012 05:35:41 -0500 (EST)*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com

On 3/6/12 at 5:57 AM, tgarza10 at msn.com (Tomas Garza) wrote: >The best I could think of is, by trial and error, to find the right >position for the horizontal line you want. The idea is to put an >Epilog in the ProbabilityScalePlot with the appropriate coordinates >for the end points, for example: ProbabilityScalePlot[{data1, data2, >data3}, "Weibull", PlotRange -> Automatic, GridLines -> Automatic, >GridLinesStyle -> "Classic", FrameLabel -> >{{Style["Ausfallwahrscheinlichkeit F(t) in %", Italic, FontSize >-> 12], ""}, {Style["Lebensdauer", Italic, FontSize -> 12], >""}}, Epilog -> {Thickness[0.005], Line[{{-3.25, 0.025}, {3.6, >0.025}}]}, Frame -> True] Or maybe you can translate from the scale >in the graph to the necessary coordinates for Line. Anyway, it looks >more or less right. -Tomas No need to use trial and error. What you have to keep in mind is the x-coordinate for the line will be Log[t] where t is the value seen on the x-axis. And the y-coordinate will be Log[-Log[1-CDF]] where CDF is the value of the cumulative distribution function. This has a particularly simple expression for the 63rd percentile of a Wiebull. At a characteristic lifetime the CDF will be 1-1/e. So, the y coordinate becomes exactly 0 in the transformed coordinate space. And since the desire is to have the line extend the full width of the plot picking the starting x coordinate to be Log[t] for any t smaller than the lowest value seen and the stop coordinate to be any t greater than the maximum value seen ensures the line extends the full width of the plot. There is no penalty for making the x-coordinates smaller/larger than shown since the PlotRange specification will prevent the line from extending too far.