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rcdf

Find x given y on cumulative frequency graph

I'm deriving a CDF from a Kernel Smoothing distribution

Here's my setup

library("DiagTest3Grp", lib.loc='~/R/win-library/3.2")

data <- c(34,46,47,48,52,53,55,56,56,56,57,58,59,59,68)
bw <- BW.ref(data)
x0 <- seq(0, 100, .1) 
KS.cdfvec <- Vectorize(KernelSmoothing.cdf, vectorize.args = "c0")
x0.cdf <- KS.cdfvec(xx = data, c0 = x0, bw = bw)
plot(x0, x0.cdf, type = "l")

Produces graph

enter image description here

Yet, I'm so green I have no idea how to derive x given y (or vice versa), I'm hoping that since it's a simple x,y graph that I just need to look up a crosssection

Solution

  • Given a value y in the CDF you want the corresponding value x in the pdf that corresponds to this. You can just use approx, but since in approx you specify yout not xout, just flip the inputs

    > approx(y=x0, x=x0.cdf, xout=0.8)
$x
[1] 0.8

$y
[1] 58.95378

    Remember that we flipped the inputs, so this means for the value 0.8 in the CDF this corresponds to a value of x=58.95378. This also assumed that is this small region of the CDF linear interpolation is a reasonable approximation.

    In the case that we have a value of x and simply want the associated value of the CDF, no argument flipping is necessary, so you can just use

    > approx(x=x0, y=x0.cdf, xout=55)
$x
[1] 55

$y
[1] 0.5090248