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

From: Duncan Murdoch <murdoch_at_stats.uwo.ca>
Date: Wed 23 Feb 2005 - 08:36:20 EST

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



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https://stat.ethz.ch/mailman/listinfo/r-devel Received on Wed Feb 23 07:43:30 2005

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