While using QQ Plots, I always notice these 'groups' of points; many sets of points arranged in a straight line and sometimes in a curve as shown below:
The theoretical quantiles are from exactly the same distribution as the simulated random vectors. I used the following R code below for these plots:
ggplot(data.frame("Theo" = sort(qnorm(ppoints(50))), "Act" = sort(rnorm(50))), aes(x = Theo, y = Act)) + geom_point(color = "#FC717F", alpha = 0.8) + labs(title = "QQPlot", x = "Theoretical Quantiles", y = "Actual Quantiles")
...but you can achieve the same result with
My question is, what is the reason for this effect?
I'm guessing that these little 'runs' happen due to some consequence of the joint order statistics distribution, but I can't figure out how/why.