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Change Log Plot scaling function

Hello all,

I want to plot Weibull distribution which is a log plot. For which I went through the demo of Log plot as shown here:

But for Weibull distribution, YAxis scale function is not just a natural logarithmic function. But its given as follows:

ln(-ln(1-p)) where p is calculated using a formula.

In short, I want to customize the log scale function for YAxis.

Please guide for some solution.

Instead of using a log scale plot the graph with normal linear scale as x vs y with y= ln(-ln(1-p)). Now the trick is to put proper yaxis ticks in position ln(-ln(1-p)) but with lable p, i.e put custom ticklabel. Check and