quantile from quantile table calculation without original data

Hallo David, Abby and Bert

Thank you for your solutions. In the meantime I found package rriskDistributions, which was able to calculate values for lognormal distribution from quantiles.

Abby

1-psolution

[1] 9.980823e-06

David

plnorm(0.1, -.7020649, .4678656)

[1] 0.0003120744

rriskDistributions

plnorm(0.1, -.6937355, .3881209)

[1] 1.697379e-05

Bert suggested to ask for original data before quantile calculation what is probably the best but also the most problematic solution. Actually, maybe original data are unavailable as it is the result from particle size measurement, where the software always twist the original data and spits only descriptive results.

All your results are quite consistent with the available values as they are close to 1, so for me, each approach works.

Thank you again.

Best regards.
Petr

-----Original Message-----
From: David Winsemius <dwinsemius at comcast.net>
Sent: Sunday, March 7, 2021 1:33 AM
To: Abby Spurdle <spurdle.a at gmail.com>; PIKAL Petr
<petr.pikal at precheza.cz>
Cc: r-help at r-project.org
Subject: Re: [R] quantile from quantile table calculation without original data


On 3/6/21 1:02 AM, Abby Spurdle wrote:

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")

Here's another approach, which uses minimization of the squared error to
get the parameters for a lognormal distribution.

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")

obj <- function(x) {sum( qlnorm(1-temp$percent, x[[1]], x[[2]])-temp$size
)^2}

# Note the inversion of the poorly named and flipped "percent" column,

optim( list(a=-0.65, b=0.42), obj)

#--------------------

$par
          a          b
-0.7020649  0.4678656

$value
[1] 3.110316e-12

$counts
function gradient
       51       NA

$convergence
[1] 0

$message
NULL


I'm not sure how principled this might be. There's no consideration in this
approach for expected sampling error at the right tail where the magnitudes
of the observed values will create much larger contributions to the sum of
squares.

--

David.

On Sat, Mar 6, 2021 at 8:09 PM Abby Spurdle <spurdle.a at gmail.com>

wrote:

I'm sorry.
I misread your example, this morning.
(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.

I'll think about it...
But someone else may come back with an answer first...


On Sat, Mar 6, 2021 at 8:17 AM Abby Spurdle <spurdle.a at 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 at 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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