🚀 go-pugleaf

I am wondering about the statistical treatment of quantile plots.
Suppose we have a quantile plot that looks linear.  This reveals
a uniform distribution.

My question is this: how can we fit a line to the points?
Linear regression won't do since the observations in a quantile
plot are not independent.  I am particularly interested in
estimating parameters of the distribution from the best fitting line
and finding confidence intervals.

I am not especially interested in the particular example of uniform
distribution.  I am interested in the general problem of fitting
curves to quantile plots.

Thanks very much for any help.

Bill Simpson