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Tony Plate

2005-Feb-22 21:44 UTC

[Rd] bug? quantile() can return decreasing sample quantiles for increasing probabilities

Is it a bug that quantile() can return a lower sample quantile for a higher 
probability?

 > ##### quantile returns decreasing results with increasing probs (data at 
the end of the message)
 > quantile(x2, (0:5)/5)
            0%           20%           40%           60%           80%
-0.0014141174 -0.0009041968 -0.0009041968 -0.0007315023 -0.0005746115
          100%
  0.2905596324
 > ##### the 40% quantile has a lower value than the 20% quantile
 > diff(quantile(x2, (0:5)/5))
           20%           40%           60%           80%          100%
  5.099206e-04 -1.084202e-19  1.726945e-04  1.568908e-04  2.911342e-01
 >

This only happens for type=7:

 > for (type in 1:9) cat(type, any(diff(quantile(x2, (0:5)/5, 
type=type))<0), "\n")
1 FALSE
2 FALSE
3 FALSE
4 FALSE
5 FALSE
6 FALSE
7 TRUE
8 FALSE
9 FALSE
 >

I know this is at the limits of machine precision, but it still seems 
wrong.  Curiously, S-PLUS 6.2 produces exactly the same numerical result on 
my machine (according to the R quantile documentation, the S-PLUS 
calculations correspond to type=7).

 > version
          _
platform i386-pc-mingw32
arch     i386
os       mingw32
system   i386, mingw32
status
major    2
minor    0.1
year     2004
month    11
day      15
language R
 >

-- Tony Plate

here's the data that gives the result above:

x2 <- c(-0.00090419678460984, -0.000980064982459659, -0.00090419678460984, 
-0.000744104385375977,
	0.206332797095889, -0.000817139943440755, -0.000899564652215867,
	-0.000574611482166109, -0.0013728312083653, -0.00090419678460984,
	-0.0013728312083653, -0.000723100843883696, -0.000630242483956473,
	-0.000817139943440755, 0.0868369624728248, -0.000817139943440755,
	-0.000817139943440755, -0.00112312180655343, -0.00112312180655343,
	-0.000380657968066988, -0.000723100843883696, -0.00090419678460984,
	-0.00090419678460984, -0.000380657968066988, -0.0010127169745309,
	-0.000723100843883696, -0.00112312180655343, -0.00112312180655343,
	-0.00090419678460984, -0.000681496801830473, -0.00090419678460984,
	-0.000380657968066988, -0.000380657968066988, -0.000817139943440755,
	-0.000723100843883696, -0.000723100843883696, -0.0013913767678397,
	-0.0013728312083653, -0.000817139943440755, -0.00112312180655343,
	-0.00112312180655343, -0.000817139943440755, 0.245683056967599,
	-0.000817139943440755, -0.00112312180655343, -0.00090419678460984,
	-0.00112312180655343, 0.123553718839373, -0.0013728312083653, 
-0.000723100843883696,
	-0.000899564652215867, 0.105625640778315, -0.00090419678460984, 
-0.0013913767678397,
	-0.00090419678460984, -0.000723100843883696, -0.000228291466122582,
	-0.00090419678460984, -0.000817139943440755, -0.00090419678460984,
	-0.000817139943440755, -0.000817139943440755, -0.000817139943440755,
	-0.000817139943440755, 0., -0.000723100843883696, -0.000380657968066988,
	-0.000723100843883696, -0.000723100843883696, -0.000899564652215867,
	-0.000764199665614537, -0.000574611482166109, -0.000681496801830473,
	-0.000817139943440755, -0.000817139943440755, -0.00090419678460984,
	-0.000723100843883696, 0.0394509065718878, -0.000817139943440755,
	-0.0013728312083653, -0.000228291466122582, -0.00090419678460984,
	-0.0013913767678397, -0.000817139943440755, -0.000817139943440755,
	-0.000817139943440755, -0.00090419678460984, -0.000681496801830473,
	-0.000817139943440755, -0.0013728312083653, -0.00090419678460984,
	-0.00112312180655343, -0.00090419678460984, -0.00112312180655343,
	-0.000723100843883696, -0.0013728312083653, -0.0013728312083653,
	-0.000574611482166109, -0.00133536543164934, -0.000369889395577567,
	-0.000723100843883696, -0.000817139943440755, -0.000723100843883696,
	-0.0013728312083653, -0.000817139943440755, -0.00090419678460984,
	-0.000723100843883696, -0.000723100843883696, -0.00090419678460984,
	-0.000723100843883696, -0.000723100843883696, -0.00090419678460984,
	-0.0010127169745309, -0.00090419678460984, -0.000723100843883696,
	-0.00090419678460984, -0.000723100843883696, -0.00090419678460984,
	-0.000817139943440755, -0.000817139943440755, -0.00138617697216216,
	-0.000574611482166109, -0.000723100843883696, 0.0238135826020014,
	-0.000723100843883696, -0.000817139943440755, -0.00090419678460984,
	-0.00112312180655343, -0.000574611482166109, -0.000380657968066988,
	-0.000723100843883696, -0.000367703891935803, -0.00090419678460984,
	-0.000574611482166109, -0.00112312180655343, -0.00090419678460984,
	0.0681528477441697, -0.000817139943440755, -0.00090419678460984,
	-0.0010127169745309, -0.00090419678460984, -0.000380657968066988,
	-0.000392709459577288, -0.0013913767678397, -0.000681496801830473,
	-0.000492947442190988, -0.00090419678460984, -0.000723100843883696,
	-0.000723100843883696, -0.000899564652215867, -0.00090419678460984,
	-0.00090419678460984, -0.00090419678460984, -0.000574611482166109,
	-0.000817139943440755, -0.000723100843883696, 0.0394509065718878, 
0.150393440609887,
	-0.00090419678460984, -0.000723100843883696, -0.000492947442190988,
	0.0514323597862607, -0.000574611482166109, -0.000681496801830473,
	-0.00090419678460984, 0.0681528477441697, 0.123553718839373, 
-0.00090419678460984,
	-0.000723100843883696, 0.0294418363344102, -0.000228291466122582, 
0.098056884039016,
	-0.000817139943440755, -0.000817139943440755, -0.00133536543164934,
	-0.000723100843883696, 0.0394509065718878, -0.00090419678460984,
	-0.00090419678460984, -0.000817139943440755, 0., -0.000228291466122582,
	-0.00090419678460984, -0.0010127169745309, -0.00133536543164934,
	-0.000723100843883696, -0.00133536543164934, -0.000817139943440755,
	-0.00090419678460984, -0.00090419678460984, -0.000723100843883696,
	-0.00090419678460984, -0.00141411735897972, -0.00090419678460984,
	-0.000817139943440755, -0.000228291466122582, -0.000817139943440755,
	-0.00139485086713518, -0.00090419678460984, 0., -0.000228291466122582,
	-0.000817139943440755, -0.0013913767678397, -0.000817139943440755,
	-0.00090419678460984, -0.000723100843883696, -0.000492947442190988,
	-0.00138617697216216, -0.00090419678460984, -0.00090419678460984,
	-0.000817139943440755, -0.0013913767678397, -0.0013728312083653,
	-0.00133536543164934, -0.00090419678460984, -0.000817139943440755,
	-0.000817139943440755, -0.000723100843883696, -0.000723100843883696,
	-0.000574611482166109, -0.00090419678460984, -0.000817139943440755,
	-0.00090419678460984, -0.000723100843883696, -0.00090419678460984,
	-0.00090419678460984, -0.000723100843883696, -0.00090419678460984,
	-0.0013913767678397, -0.000681496801830473, -0.000817139943440755,
	-0.00107976084663754, -0.0013728312083653, -0.00090419678460984,
	-0.0013728312083653, -0.00090419678460984, 0.0394509065718878, 
-0.00090419678460984,
	-0.0013913767678397, 0., -0.000817139943440755, 0.121526161829631,
	-0.0013728312083653, -0.00090419678460984, -0.000723100843883696,
	-0.000817139943440755, -0.00090419678460984, -0.000817139943440755,
	-0.0013728312083653, -0.000723100843883696, -0.000817139943440755,
	-0.00090419678460984, -0.000574611482166109, -0.00090419678460984,
	-0.000817139943440755, -0.0013913767678397, -0.000723100843883696,
	-0.000817139943440755, -0.0010127169745309, 0.098056884039016, 
0.0394509065718878,
	-0.000380657968066988, -0.000817139943440755, -0.0010127169745309,
	-0.0010127169745309, -0.00090419678460984, -0.000817139943440755,
	-0.000574611482166109, -0.00090419678460984, -0.000723100843883696,
	-0.000723100843883696, -0.000681496801830473, -0.000723100843883696,
	-0.0013728312083653, -0.000723100843883696, 0.276647976466588, 
-0.0013913767678397,
	-0.000817139943440755, -0.00090419678460984, -0.000817139943440755,
	-0.00090419678460984, -0.00090419678460984, -0.000723100843883696,
	-0.000723100843883696, -0.00090419678460984, 0.098056884039016,
	-0.000723100843883696, -0.000723100843883696, -0.000817139943440755,
	-0.0010127169745309, -0.00090419678460984, -0.000658830006917318,
	-0.000380657968066988, -0.000723100843883696, 0.245683056967599,
	-0.000723100843883696, -0.000723100843883696, -0.000723100843883696,
	-0.000817139943440755, -0.000723100843883696, -0.0013728312083653,
	-0.000817139943440755, -0.0013728312083653, -0.0013728312083653,
	-0.00090419678460984, -0.000723100843883696, -0.000574611482166109,
	-0.00090419678460984, -0.000817139943440755, -0.000392709459577288,
	-0.0013728312083653, -0.000723100843883696, 0.0681528477441697,
	-0.000380657968066988, -0.000723100843883696, -0.000723100843883696,
	-0.000574611482166109, -0.000723100843883696, -0.0013728312083653,
	0.0394509065718878, -0.000817139943440755, -0.000817139943440755,
	-0.000723100843883696, -0.000723100843883696, -0.00090419678460984,
	-0.000817139943440755, -0.000817139943440755, -0.000723100843883696,
	-0.00090419678460984, -0.000817139943440755, -0.000723100843883696,
	0.0394509065718878, -0.000817139943440755, -0.00090419678460984,
	-0.0013728312083653, -0.00090419678460984, -0.00090419678460984,
	0.000261948222205752, -0.000817139943440755, -0.00112312180655343,
	-0.00138617697216216, -0.000723100843883696, -0.000817139943440755,
	-0.00090419678460984, -0.000574611482166109, -0.000723100843883696,
	-0.000817139943440755, -0.000492947442190988, -0.000817139943440755,
	-0.000723100843883696, -0.000574611482166109, -0.000723100843883696,
	-0.000574611482166109, -0.000380657968066988, -0.0013913767678397,
	-0.000744104385375977, -0.0013728312083653, -0.00090419678460984,
	0.0294418363344102, -0.000817139943440755, 0., -0.00112312180655343,
	-0.000723100843883696, -0.00090419678460984, -0.00112312180655343,
	-0.000723100843883696, 0.000261948222205752, -0.00090419678460984,
	-0.00112312180655343, -0.000228291466122582, -0.0010127169745309,
	-0.00090419678460984, -0.00112312180655343, -0.000723100843883696,
	-0.00090419678460984, -0.000723100843883696, -0.00112312180655343,
	-0.00112312180655343, -0.000392709459577288, -0.00090419678460984,
	-0.000380657968066988, 0.055351421946571, -0.00090419678460984,
	-0.000817139943440755, -0.000723100843883696, -0.000817139943440755,
	-0.0013728312083653, -0.000723100843883696, -0.000817139943440755,
	0.142219055266607, -0.0010127169745309, -0.00090419678460984, 
0.150393440609887,
	-0.00090419678460984, 0.0394509065718878, -0.000108088765825544,
	-0.000363934607732864, -0.00090419678460984, -0.000658830006917318,
	0.000261948222205752, -0.0013913767678397, -0.000228291466122582,
	-0.000723100843883696, -0.00107976084663754, -0.00112312180655343,
	-0.0013913767678397, -0.00090419678460984, -0.000369889395577567,
	-0.000366074698311942, -0.000817139943440755, -0.00090419678460984,
	-0.00112312180655343, -0.000723100843883696, -0.000817139943440755,
	-0.000723100843883696, -0.00090419678460984, -0.00090419678460984,
	-0.0013913767678397, -0.0013913767678397, 0.29055963243757, 
-0.0013913767678397,
	-0.00090419678460984, -0.00107976084663754, -0.0013728312083653,
	-0.00090419678460984, -0.0013913767678397, -0.000817139943440755,
	-0.000723100843883696, -0.000817139943440755, -0.00112312180655343,
	0.000261948222205752, -0.000817139943440755, -0.000817139943440755,
	-0.00090419678460984, -0.000574611482166109, -0.000363934607732864,
	-0.000380657968066988, -0.000723100843883696, -0.000574611482166109,
	-0.00090419678460984, -0.000723100843883696, -0.00090419678460984,
	0.000261948222205752, -0.000681496801830473, -0.000723100843883696,
	-0.000681496801830473, -0.000723100843883696, -0.0013728312083653,
	-0.0013728312083653, -0.000980064982459659, -0.000817139943440755,
	0.0142179188274202, -0.000574611482166109, -0.000817139943440755,
	-0.00090419678460984, 0.0864739531562442, -0.000723100843883696,
	-0.00090419678460984, -0.00133536543164934, -0.000817139943440755,
	-0.0013728312083653, -0.000228291466122582, -0.000817139943440755,
	-0.00112312180655343, -0.00090419678460984, -0.00138617697216216,
	-0.00090419678460984, -0.00080565611521403, -0.000817139943440755,
	-0.00133536543164934, -0.000817139943440755, -0.0013913767678397,
	-0.0013913767678397, 0., -0.00112312180655343, -0.000723100843883696,
	-0.000817548661004929, -0.000723100843883696, -0.00090419678460984,
	-0.00090419678460984, -0.000817139943440755, 0.232276121775309, 
-0.0013728312083653,
	-0.00090419678460984, -0.000817139943440755, -0.000723100843883696,
	-0.000817139943440755, -0.0013913767678397, -0.000380657968066988, 0.,
	-0.000744104385375977, -0.00090419678460984, -0.00138617697216216,
	-0.000621216637747628, -0.000817139943440755, -0.000817139943440755,
	-0.000723100843883696, -0.000817139943440755, -0.000817139943440755,
	-0.00112312180655343, -0.000574611482166109, -0.000723100843883696,
	-0.000367703891935803, -0.000228291466122582, -0.000723100843883696,
	0.185858022598993, -0.000723100843883696, -0.00090419678460984, 
0.0394509065718878,
	0.0142179188274202, -0.000492947442190988, -0.000492947442190988,
	-0.00090419678460984, -0.000817139943440755, -0.00112312180655343,
	-0.000723100843883696, -0.00133536543164934, -0.00090419678460984,
	-0.0013728312083653, -0.0013728312083653, -0.000574611482166109,
	-0.000817548661004929, -0.000228291466122582, -0.00112312180655343,
	-0.00090419678460984, -0.000817139943440755, -0.00090419678460984,
	-0.000817139943440755, -0.000621216637747628, -0.00090419678460984,
	-0.000380657968066988, -0.00112312180655343, -0.00090419678460984,
	-0.000723100843883696, -0.000817139943440755, -0.000574611482166109,
	-0.00090419678460984, -0.00080565611521403, -0.00090419678460984,
	-0.000574611482166109, -0.0010127169745309, -0.0010127169745309,
	-0.000574611482166109, -0.0013728312083653, -0.00090419678460984,
	-0.00090419678460984, -0.000658830006917318, -0.000817139943440755,
	-0.00090419678460984, -0.0010127169745309, 0.0394509065718878,
	-0.000817139943440755, 0.132284868331183, -0.00090419678460984, 
-0.0013728312083653,
	-0.000817139943440755, -0.000744104385375977, -0.000817139943440755,
	-0.0013913767678397, -0.00090419678460984, -0.00090419678460984,
	-0.000817139943440755, -0.000817139943440755, 0.0142179188274202,
	0.0258830842517671, -0.000723100843883696, -0.000681496801830473,
	-0.000706127711704799, 0.000261948222205752, -0.00090419678460984,
	-0.000723100843883696, -0.00112312180655343, -0.000817139943440755,
	-0.000817139943440755, -0.00133536543164934, -0.000723100843883696,
	-0.000380657968066988, -0.000723100843883696, -0.00107976084663754,
	-0.00090419678460984, -0.00090419678460984, -0.0013728312083653,
	-0.000681496801830473, -0.00090419678460984, -0.0013728312083653,
	-0.000817139943440755, -0.000723100843883696, -0.000817139943440755,
	-0.000723100843883696, -0.000723100843883696, -0.000817139943440755,
	-0.000817139943440755, -0.00090419678460984, -0.000817139943440755,
	-0.000380657968066988, -0.00090419678460984, -0.000723100843883696,
	-0.000817139943440755, -0.0013728312083653, -0.000723100843883696,
	-0.00090419678460984, -0.000681496801830473)

Duncan Murdoch

2005-Feb-22 22:36 UTC

head link

[Rd] bug? quantile() can return decreasing sample quantiles for increasing probabilities

On Tue, 22 Feb 2005 13:43:47 -0700, Tony Plate
<tplate@blackmesacapital.com> wrote :
>Is it a bug that quantile() can return a lower sample quantile for a higher 
>probability?
>
> > ##### quantile returns decreasing results with increasing probs (data
at
>the end of the message)
> > quantile(x2, (0:5)/5)
>            0%           20%           40%           60%           80%
>-0.0014141174 -0.0009041968 -0.0009041968 -0.0007315023 -0.0005746115
>          100%
>  0.2905596324
> > ##### the 40% quantile has a lower value than the 20% quantile
> > diff(quantile(x2, (0:5)/5))
>           20%           40%           60%           80%          100%
>  5.099206e-04 -1.084202e-19  1.726945e-04  1.568908e-04  2.911342e-01
> >
>
>This only happens for type=7:
>
> > for (type in 1:9) cat(type, any(diff(quantile(x2, (0:5)/5, 
>type=type))<0), "\n")
>1 FALSE
>2 FALSE
>3 FALSE
>4 FALSE
>5 FALSE
>6 FALSE
>7 TRUE
>8 FALSE
>9 FALSE
> >
>
>I know this is at the limits of machine precision, but it still seems 
>wrong.  Curiously, S-PLUS 6.2 produces exactly the same numerical result on 
>my machine (according to the R quantile documentation, the S-PLUS 
>calculations correspond to type=7).
I'd say it's not a bug in that rounding error is something you should
expect in a calculation like this, but it does look wrong.  And it
isn't only restricted to type 7.  If you make a vector of copies of
that bad value, you'll see it in more cases:
> x <- rep(-0.00090419678460984, 602)
> for (type in 1:9) cat(type, any(diff(quantile(x, (0:5)/5, + type=type))<0), "\n")
1 FALSE 
2 FALSE 
3 FALSE 
4 FALSE 
5 TRUE 
6 TRUE 
7 TRUE 
8 FALSE 
9 TRUE 

(at least on Windows).  What's happening is that R is doing linear
interpolation between two equal values, and not getting the same value
back, because of rounding.  

The offending line appears to be this one:

qs[i] <- ifelse(h == 0, qs[i], (1 - h) * qs[i] + h * x[hi[i]])

The equivalent calculation in the approx function (which doesn't
appear to have this problem) is

qs[i] + (x[hi[i]] - qs[i]) * h

Can anyone think of why this would not be better?  (The same sort of
calculation shows up again later in quantile().)

Duncan Murdoch

R devel - Feb 2005 - bug? quantile() can return decreasing sample quantiles for increasing probabilities

[Rd] bug? quantile() can return decreasing sample quantiles for increasing probabilities

[Rd] bug? quantile() can return decreasing sample quantiles for increasing probabilities