PIKAL Petr
2021-Mar-05 09:14 UTC
[R] quantile from quantile table calculation without original data
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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Jeff Newmiller
2021-Mar-05 18:09 UTC
[R] quantile from quantile table calculation without original data
Your example could probably be resolved with approx. If you want a more robust solution, it looks like the fBasics package can do spline interpolation. You may want to spline on the log of your size variable and use exp on the output if you want to avoid negative results. On March 5, 2021 1:14:22 AM PST, 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 >Osobn? ?daje: Informace o zpracov?n? a ochran? osobn?ch ?daj? >obchodn?ch partner? PRECHEZA a.s. jsou zve?ejn?ny na: >https://www.precheza.cz/zasady-ochrany-osobnich-udaju/ | Information >about processing and protection of business partner's personal data are >available on website: >https://www.precheza.cz/en/personal-data-protection-principles/ >D?v?rnost: Tento e-mail a jak?koliv k n?mu p?ipojen? dokumenty jsou >d?v?rn? a podl?haj? tomuto pr?vn? z?vazn?mu prohl?en? o vylou?en? >odpov?dnosti: https://www.precheza.cz/01-dovetek/ | This email and any >documents attached to it may be confidential and are subject to the >legally binding disclaimer: https://www.precheza.cz/en/01-disclaimer/ > > > [[alternative HTML version deleted]]-- Sent from my phone. Please excuse my brevity.
David Winsemius
2021-Mar-05 18:23 UTC
[R] quantile from quantile table calculation without original data
On 3/5/21 1:14 AM, PIKAL Petr 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.The quantiles are in reverse order so tryoing to match the data to quantiles from candidate parameters requires subtracting them from unity: > temp$size [1] 1.6000 0.9466 0.8062 0.6477 0.5069 0.3781 0.3047 0.2681 0.1907 > qlnorm(1-temp$percent, -.5) [1] 6.21116124 3.14198142 2.18485959 1.19063854 0.60653066 0.30897659 0.16837670 0.11708517 0.05922877 > qlnorm(1-temp$percent, -.9) [1] 4.16346589 2.10613313 1.46455518 0.79810888 0.40656966 0.20711321 0.11286628 0.07848454 0.03970223 > qlnorm(1-temp$percent, -2) [1] 1.38589740 0.70107082 0.48750807 0.26566737 0.13533528 0.06894200 0.03756992 0.02612523 0.01321572 > qlnorm(1-temp$percent, -1.6) [1] 2.06751597 1.04587476 0.72727658 0.39632914 0.20189652 0.10284937 0.05604773 0.03897427 0.01971554 > qlnorm(1-temp$percent, -1.6, .5) [1] 0.64608380 0.45951983 0.38319004 0.28287360 0.20189652 0.14410042 0.10637595 0.08870608 0.06309120 > qlnorm(1-temp$percent, -1, .5) [1] 1.1772414 0.8372997 0.6982178 0.5154293 0.3678794 0.2625681 0.1938296 0.1616330 0.1149597 > qlnorm(1-temp$percent, -1, .4) [1] 0.9328967 0.7103066 0.6142340 0.4818106 0.3678794 0.2808889 0.2203318 0.1905308 0.1450700 > qlnorm(1-temp$percent, -0.5, .4) [1] 1.5380866 1.1710976 1.0127006 0.7943715 0.6065307 0.4631076 0.3632657 0.3141322 0.2391799 > qlnorm(1-temp$percent, -0.55, .4) [1] 1.4630732 1.1139825 0.9633106 0.7556295 0.5769498 0.4405216 0.3455491 0.2988118 0.2275150 > qlnorm(1-temp$percent, -0.55, .35) [1] 1.3024170 1.0260318 0.9035201 0.7305712 0.5769498 0.4556313 0.3684158 0.3244257 0.2555795 > qlnorm(1-temp$percent, -0.55, .45) [1] 1.6435467 1.2094723 1.0270578 0.7815473 0.5769498 0.4259129 0.3241016 0.2752201 0.2025322 > qlnorm(1-temp$percent, -0.53, .45) [1] 1.6767486 1.2339052 1.0478057 0.7973356 0.5886050 0.4345169 0.3306489 0.2807799 0.2066236 > qlnorm(1-temp$percent, -0.57, .45) [1] 1.6110023 1.1855231 1.0067207 0.7660716 0.5655254 0.4174793 0.3176840 0.2697704 0.1985218 Seems like it might be an acceptable fit. modulo the underlying data gathering situation which really should be considered. You can fiddle with that result. My statistical hat (not of PhD level certification) says that the middle quantiles in this sequence probably have the lowest sampling error for a lognormal, but I'm rather unsure about that. A counter-argument might be that since there is a hard lower bound of 0 for the 0-th quantile that you should be more worried about matching the 0.1907 value to the 0.01 order statistic, since 99% of the data is know to be above it. Seems like efforts at matching the 0.50 quantile to 0.5069 for the logmean parameter and matching the 0.01 quantile 0.1907 for estimation of? the variance estimate might be preferred to worrying too much about the 1.6 value which would be in the right tail (and far away from your region of extrapolation.) Further trial and error: > qlnorm(1-temp$percent, -0.58, .47) [1] 1.6709353 1.2129813 1.0225804 0.7687497 0.5598984 0.4077870 0.3065638 0.2584427 0.1876112 > qlnorm(1-temp$percent, -0.65, .47) [1] 1.5579697 1.1309763 0.9534476 0.7167775 0.5220458 0.3802181 0.2858382 0.2409704 0.1749275 > qlnorm(1-temp$percent, -0.65, .5) [1] 1.6705851 1.1881849 0.9908182 0.7314290 0.5220458 0.3726018 0.2750573 0.2293682 0.1631355 > qlnorm(1-temp$percent, -0.65, .4) [1] 1.3238434 1.0079731 0.8716395 0.6837218 0.5220458 0.3986004 0.3126657 0.2703761 0.2058641 > qlnorm(1-temp$percent, -0.68, .4) [1] 1.2847179 0.9781830 0.8458786 0.6635148 0.5066170 0.3868200 0.3034251 0.2623852 0.1997799 > qlnorm(1-temp$percent, -0.65, .39) [1] 1.2934016 0.9915290 0.8605402 0.6791257 0.5220458 0.4012980 0.3166985 0.2748601 0.2107093 > > qlnorm(1-temp$percent, -0.65, .42) [1] 1.3868932 1.0416839 0.8942693 0.6930076 0.5220458 0.3932595 0.3047536 0.2616262 0.1965053 > qlnorm(1-temp$percent, -0.68, .42) [1] 1.3459043 1.0108975 0.8678396 0.6725261 0.5066170 0.3816369 0.2957468 0.2538940 0.1906976 (I did make an effort at searching for quantile matching as a method for distribution fitting, but came up empty.) -- David.> > Please, give me some hint where to look. > > > Best regards > > Petr>[[alternative HTML version deleted]]
Abby Spurdle
2021-Mar-05 19:17 UTC
[R] quantile from quantile table calculation without original data
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 > Osobn? ?daje: Informace o zpracov?n? a ochran? osobn?ch ?daj? obchodn?ch partner? PRECHEZA a.s. jsou zve?ejn?ny na: https://www.precheza.cz/zasady-ochrany-osobnich-udaju/ | Information about processing and protection of business partner's personal data are available on website: https://www.precheza.cz/en/personal-data-protection-principles/ > D?v?rnost: Tento e-mail a jak?koliv k n?mu p?ipojen? dokumenty jsou d?v?rn? a podl?haj? tomuto pr?vn? z?vazn?mu prohl??en? o vylou?en? odpov?dnosti: https://www.precheza.cz/01-dovetek/ | This email and any documents attached to it may be confidential and are subject to the legally binding disclaimer: https://www.precheza.cz/en/01-disclaimer/ > > > [[alternative HTML version deleted]] > > ______________________________________________ > R-help at r-project.org mailing list -- To UNSUBSCRIBE and more, see > https://stat.ethz.ch/mailman/listinfo/r-help > PLEASE do read the posting guide http://www.R-project.org/posting-guide.html > and provide commented, minimal, self-contained, reproducible code.