[R] Exact quantile regression
Per Bak
perbak at tdcadsl.dk
Thu May 5 15:37:07 CEST 2005
Hi,
I have been returning to the same problem a number of times without success
and now look for help with the following:
How do I fit a distribution function with the same number of parameters as
there are quantiles and values such that I get an exact solution as opposed
to a minimum least squares type solution? Say, which lognormal distribution
has a 15% quantile of 10 and a 50% quantile of 30? My hope is that the
solution to this problem can be expanded, such that I can fit three quantiles
with the Generalized Weibull distribution (which has three parameters).
This is what I attempt without success:
=======================
library(stats)
Target <- data.frame(
quantiles = c(0.15, 0.50),
values = c(10, 30))
dist <- nls(values ~ qlnorm(quantiles, mu, sd), data = Target,
start = list(mu = 30, sd = 5))
I can see that it works with one more value:
==========================
Target <- data.frame(
quantiles = c(0.15, 0.50, 0.85),
values = c(10, 30, 60))
dist <- nls(values ~ qlnorm(quantiles, mu, sd), data = Target,
start = list(mu = 30, sd = 5))
Kind regards,
Per Bak
Copenhagen, Denmark
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