qqplot against theoretical quantiles

Question

I want to be able to do qqplots against theoretical quantiles. I already know qqnorm() does that for the normal distribution, but that's a pretty a limited tool to me. Also, I noticed that some people simulate random processes from a given distribution and use it to compare to sample data, which is not entirely rigorous because it depends on the method of simulation. So my example would be to compare sample data to geometric distribution:

#sample data
var=rgeom(prob=0.3, n=100)

#QQplot against a theoretical geometric distribution with prob=0.5

score 1 · Accepted Answer · edited May 23 '17 at 10:25

1

You can produce such a plot easily with the ggplot2 package:

library(ggplot2)
qplot(sample = var, geom = "point", stat = "qq", 
      distribution = qgeom, dparams = list(prob = 0.5))

The theoretical quantiles (x axis) are derived from a geometric distribution with a probability of 0.5. enter image description here

Update (based on question in comment):

A line can be added in the following way though it is not very well suited for geometric distribution. The approach is based on this answer.

qv <- quantile(var, c(.25, .75))
qt <- qgeom(prob = 0.5, c(.25, .75))
slope <- diff(qv)/diff(qt)
int <- qv[1] - slope * qt[1]

qplot(sample = var, geom = "point", stat = "qq", 
      distribution = qgeom, dparams = list(prob = 0.5)) + 
  geom_abline(slope = slope, intercept = int)

enter image description here

edited May 23 '17 at 10:25

Community

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answered Feb 06 '14 at 18:54

Sven Hohenstein

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Nice, how do I add that classical bisection line? – user3083324 Feb 06 '14 at 19:59
@user3083324 This line doesn't make much sense for your distributions. However, have a look at the update. – Sven Hohenstein Feb 06 '14 at 20:14
OP's `var` is taken from `rgeom(...)` with prob=0.3, your plots have prob=0.5. – jlhoward Feb 06 '14 at 20:27
@jlhoward Have a look at the question (in particular the last line). – Sven Hohenstein Feb 06 '14 at 20:38
As u lower the theoretical prob parameter the closer the line gets to the points. – user3083324 Feb 06 '14 at 20:58
@user3083324 This behaviour is not surprising. Since your random data are based on a probability of 0.3, you will get the closest match between both distributions when the theoretical quantiles are based on a probability of 0.3 too. – Sven Hohenstein Feb 06 '14 at 21:02
I know! I was answering ur previous point about the tail of the distribution. – user3083324 Feb 06 '14 at 21:22

score 0 · Answer 2 · answered Feb 06 '14 at 18:47

0

A Q-Q plot is a plot of quantiles of a ramdom sample against quantiles of the test distribution. So,

plot(qgeom(seq(0,1,length=100),.3),quantile(var,seq(0,1,length=100)))

answered Feb 06 '14 at 18:47

jlhoward

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qqplot against theoretical quantiles

2 Answers2