Hi again,
I think we've been thinking about this wrong.? You apparently want to
report the mean for the period 23:10:00 - 23:20:00 from 1-second samples
(sampled on the second).? This amounts to integrating over the 10-minute
period (multiply each sample by the time interval it represents) and
dividing by 10 minutes..? For a case like this, elementary approaches to
estimating the integral make use of *both* end points.? The Trapezoid
Rule, for example, weights each of the samples equally except the two
end points, which get half the weight.
So,? your bounds should define the interval represented by the mean you
are reporting (23:10:00 - 23:20:00), and you should estimate that mean
using 601 samples, but weighting the first and last sample half as much
as the others.
best regards,
Karl
On 3/26/18 9:00 AM, Karl Taylor wrote:
> Dear Erik,
>
> I think one could argue that a "sample" taken *on* the second is most
> representative of an interval extending from half a second prior to
> the sample time and half a second following the sample time, so, for
> example, a sample at 1 sec represents the interval from 0.5 to 1.5
> seconds.? In that case if your 1st sample is at 23:10:00 and last
> sample is at 23:19:59, you might want to set the bounds on your
> 10-minute mean as 23:09:59.5 and 23:19:59.5.
>
> On the other hand, if there is some finite response response time of
> your instrument (say, of order 1 sec), you could argue that a sample
> taken at time t really represents an average over some preceding
> interval, and then you might say your 10-minute mean extends from
> 23:09:59 to 23:19:59.? In this case I would be tempted to compute
> 10-minute means from samples starting with 23:10:01and ending with
> 23:20:00, so the bounds would be 23:10:00 and 23:20:00.
>
> In any case the bounds should span exactly 10 minutes, I think.
>
> These suggestions come from someone? unfamiliar with observational
> protocols, so take them for what they're worth.
>
> regards,
> Karl
>
> On 3/26/18 7:26 AM, Jim Biard wrote:
>> Erik,
>>
>> Bounds are always inclusive lower / exclusive upper. That's [low,
>> high) in common notation. If the cells abut one another, the upper
>> bound for one should be identical to the lower bound for then next.
>>
>> Grace and peace,
>>
>> Jim
>>
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>>
>> On Mon, Mar 26, 2018 at 4:29 AM, Erik Quaeghebeur
>> <E.R.G.Quaeghebeur at tudelft.nl <mailto:E.R.G.Quaeghebeur at tudelft.nl>>
>> wrote:
>>
>> Dear list,
>>
>>
>> Is there a standard way to indicate which bounds are included in
>> a bounds variable?
>>
>> Context: I have 10-min. statistics, e.g., the mean of 600
>> per-second samples from 23:10:00 to 23:19:59. Currently, in my
>> bounds variable for time, I have, essentially, [23:10:00,
>> 23:20:00]. I list my time in seconds since 1970-01-01. Should I
>> use [23:10:00, 23:19:59] instead?
>>
>>
>> Best,
>>
>> Erik
>>
>> --
>> https://ac.erikquaeghebeur.name <https://ac.erikquaeghebeur.name>
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