TransWikia.com

How can I determine and then plot a confidence bands in QuantilePlot?

Mathematica Asked on February 7, 2021

Does anyone know if its possible to plot a confidence band in QuantilePlot? I haven’t been able to find any documentation for this, or a previous example on here.

At the moment the only way I can think of doing this is via simulation or bootstrapping, which I’d like to avoid.


I’ve made an attempt based in some of the resources posted in the comments. This give a simultaneous confidence band:

n = 64;
X = RandomVariate[NormalDistribution[0, 1], n];
μ = Mean[X];
σ = StandardDeviation[X];
α = 0.05 (* For a 100(1-α)% simultaneous confidence band *)
k = Sqrt[Log[2/α]/(2 n)]  (* Good when n > 35 *)
Show[
        {
            QuantilePlot[X, NormalDistribution[Mean[X], StandardDeviation[X]],ImageSize->Automatic->200, LabelStyle->12, PlotStyle->Red],
            ListPlot[Table[{x, InverseCDF[NormalDistribution[μ, σ], 1/Length[X] Length[Select[X, # <= x &]] - k]}, {x, X}], PlotRange->All],
            ListPlot[Table[{x, InverseCDF[NormalDistribution[μ, σ], 1/Length[X] Length[Select[X, # <= x &]] + k]}, {x, X}], PlotRange->All]
        }, PlotRange->All
    ]

QQ plot and simultaneous confidence band

Add your own answers!

Ask a Question

Get help from others!

© 2024 TransWikia.com. All rights reserved. Sites we Love: PCI Database, UKBizDB, Menu Kuliner, Sharing RPP