# [R] quantile from quantile table calculation without original data

Abby Spurdle @purd|e@@ @end|ng |rom gm@||@com
Sat Mar 6 10:02:25 CET 2021

```I came up with a solution.
But not necessarily the best solution.

I used a spline to approximate the quantile function.
Then use that to generate a large sample.
(I don't see any need for the sample to be random, as such).
Then compute the sample mean and sd, on a log scale.
Finally, plug everything into the plnorm function:

p <- seq (0.01, 0.99,, 1e6)
Fht <- splinefun (temp\$percent, temp\$size)
x <- log (Fht (p) )
psolution <- plnorm (0.1, mean (x), sd (x), FALSE)
psolution

The value of the solution is very close to one.
Which is not a surprise.

Here's a plot of everything:

u <- seq (0.000001, 1.65,, 200)
v <- plnorm (u, mean (x), sd (x), FALSE)
plot (u, v, type="l", ylim = c (0, 1) )
points (temp\$size, temp\$percent, pch=16)
points (0.1, psolution, pch=16, col="blue")

On Sat, Mar 6, 2021 at 8:09 PM Abby Spurdle <spurdle.a using gmail.com> wrote:
>
> I'm sorry.
> (I didn't read the code after the line that calls plot).
>
> After looking at this problem again, interpolation doesn't apply, and
> extrapolation would be a last resort.
> If you can assume your data comes from a particular type of
> distribution, such as a lognormal distribution, then a better approach
> would be to find the most likely parameters.
>
> i.e.
> This falls within the broader scope of maximum likelihood.
> (Except that you're dealing with a table of quantile-probability
> pairs, rather than raw observational data).
>
> I suspect that there's a relatively easy way of finding the parameters.
>
> But someone else may come back with an answer first...
>
>
> On Sat, Mar 6, 2021 at 8:17 AM Abby Spurdle <spurdle.a using gmail.com> wrote:
> >
> > I note three problems with your data:
> > (1) The name "percent" is misleading, perhaps you want "probability"?
> > (2) There are straight (or near-straight) regions, each of which, is
> > equally (or near-equally) spaced, which is not what I would expect in
> > problems involving "quantiles".
> > (3) Your plot (approximating the distribution function) is
> > back-the-front (as per what is customary).
> >
> >
> > On Fri, Mar 5, 2021 at 10:14 PM PIKAL Petr <petr.pikal using precheza.cz> wrote:
> > >
> > > Dear all
> > >
> > > I have table of quantiles, probably from lognormal distribution
> > >
> > >  dput(temp)
> > > temp <- structure(list(size = c(1.6, 0.9466, 0.8062, 0.6477, 0.5069,
> > > 0.3781, 0.3047, 0.2681, 0.1907), percent = c(0.01, 0.05, 0.1,
> > > 0.25, 0.5, 0.75, 0.9, 0.95, 0.99)), .Names = c("size", "percent"
> > > ), row.names = c(NA, -9L), class = "data.frame")
> > >
> > > and I need to calculate quantile for size 0.1
> > >
> > > plot(temp\$size, temp\$percent, pch=19, xlim=c(0,2))
> > > ss <- approxfun(temp\$size, temp\$percent)
> > > points((0:100)/50, ss((0:100)/50))
> > > abline(v=.1)
> > >
> > > If I had original data it would be quite easy with ecdf/quantile function but without it I am lost what function I could use for such task.
> > >
> > > Please, give me some hint where to look.
> > >
> > >
> > > Best regards
> > >
> > > Petr
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