# [R] Finding Lower Envelope of Points on a Plot?

(Ted Harding) Ted.Harding at manchester.ac.uk
Wed Jun 30 23:26:57 CEST 2010

```I think this has reached the point where it is absolutely necessary
for Asha Sharma to state *exactly* what is meant by a "linear lower
envelope" of a set of points. There are too many possibilities for
the problem as stated so far. For instance (possibilities which have
not been considered so far):

[1] A straight line which is such that any point which falls below
it is "censored" and so would not be present (but this would seem
to be inconsistent with Asha's proviso of "a specified percentage
of points allowed to lie outside it");

[2] A line parallel to the regression line, but displaced downwards
in such a way as to exclude a ceretain percantage of ths points
(i.e. such that that percentage lie below the line); but this does
not match my own usual interpretation of "envelope" (which is such
that it is a boundary for the positions of the points, as in [1]).

And so on ...
Ted.

On 30-Jun-10 20:58:45, David Winsemius wrote:
> On Jun 30, 2010, at 4:02 PM, Asha Sharma wrote:
>> Hi,
>> Thanks to both of you for taking the time to answer my question. I
>> was maybe not very clear in the way I framed my question. By plot, I
>> meant an x-y plot with a cloud of points which should have a linear
>> lower envelope. Is there a way to both plot as well as get the
>> parameters of the lower envelope (intercept, slope, etc.) and to
>> also set the percentage of points outside it?
>
> I suspect you are requesting a scatterplot with a superimposed linear
> fit and 5% and 95% prediction intervals. Not much point in pursuing
> until you "confirm or deny".
>
> --
> David
>>
>> Thanks!
>>
>> Asha
>>
>>
>> Stephan Kolassa wrote:
>>> Hi,
>>>
>>> one possibility would be to calculate the convex hull using
>>> chull(). I believe that the hull points are returned by chull() in
>>> a clockwise order (?), so the points between the rightmost and the
>>> leftmost point in the chull() result are the lower half of the
>>> convex hull. Remove these points from the original dataset (a
>>> variant of "peeling convex hulls") and iterate until you have
>>> removed your prespecified percentage of points - these all lie
>>> outside of the final lower hull (though the percentage will, of
>>> course, only be approximated, but you should be able to modify this
>>> to taste).
>>>
>>> HTH
>>> Stephan
>>>
>>>
>>> David Winsemius schrieb:
>>>>
>>>> On Jun 30, 2010, at 2:05 PM, Asha Sharma wrote:
>>>>
>>>>> Hi,
>>>>>
>>>>> I am looking for a way to find the lower envelope of points on a
>>>>> plot, preferably specifying what percentage of points should be
>>>>> allowed to lie outside the envelope. There must be a
>>>>> straightforward way to do this, but I do not seem to be able to
>>>>> find it. I would greatly appreciate any help.
>>>>
>>>> You probably want something like the "lower half" of the convex
>>>> hull. You should find quite a bit of code with your favorite r
>>>> search engine on the topic of "convex hull".
>>>
>>
>
> David Winsemius, MD
> West Hartford, CT

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Date: 30-Jun-10                                       Time: 22:26:54
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