Newsgroup sci.stat.math 14468

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In article <01bc80f6$574b6400$dbb2d4d0@bwheeler>, "Bob Wheeler"
 wrote:
> The medians of size n samples have a distribution
> whose spread depends on n.  The variance for a 
> normal distribution is (1.25 SD/sqrt(n))^2. The mean is a
> more efficient estimator with variance (SD/sqrt(n))^2
Agreed.
> hence 
> nothing will be gained by using the median, although for
> the simple purposes of the original poster, the median
> divided by the range will no doubt work as well.
No, this isn't right. The fact the median is a less efficient estimator of
central tendency is precisely the reason it is the better choice. Being
less efficient means the median is converges more slowly as observations
are added, i.e., it is less sensitive to an extreme observation.
Dividing the median by the range does add weight for consistent play. It
also means a good player might rank lower as a result of one hot game than
a consistent but poorer player. I doubt this would be considered
acceptable for most people as a ranking system.
If the total number of games is fairly large it is likely ranking
according to median score will be the same as ranking by average score.
For a small number of games there is a much better chance there will be a
significant difference between the two methods.

Harry Sommer wrote:
  > in an image processing book I read of a butterworth radially 
  > symmetric bandpass filter and this is exactly what I need for my 
  > filter problem. Unfortunately I do not know how the formula of such 
  > butterworth bandpass filter looks like. So it would be very helpful 
  > if someone can give me the formula.
In the frequency domain, the response of a Butterworth filter has the
form
          B(f) = 1/(1 + (f/c)**n) ,
where f represents frequency, c is an adjustable parameter that
determines the frequency at which the filter's response falls to half of
its value at f = 0, and n is an adjustable parameter that determines how
sharply the filter's response decreases in the neighborhood of f = c.
   Charles Metz

Being totally unfamilair with stats, but having to complete a dissertation involving some statistical analysis, I was wondering if anyone can advise on what test and what data would need to be collected for my particular line of work.
The area I am looking at has three soil types running. Type 1 is in the north, type tw0 middle, type three the most southerly. Three species of tree occur over the entire area, although there appears to be a relationship between tree type and underlying soil type. My hope was to study the density of each tree species in relationship to soil type and then somehow look at age distb. as well.
Having been browing through various stat.technique books on the variey of stat. techniques avaialble I'm more confused than ever. Can anyone e-mail with advise as to the best way to approach the above problem? All suggestions greatly appreciated!!!!!
Richard

Hi,
Does anyone know to calculate the expectation 
of the sample third moment
m3=1/n \sum_{i \in s} (y_i - \bar y)^3
when sampling is done: 
- with replacement?
- without replacement?
Do you know where can I find such demonstration?
Best wishes,
Julio
====================================================================
Julio Cesar Cabeca		jucabeca@ulb.ac.be
LMTD-ULB / CP 124		tel. (+32-2) 650.34.61
Av. Jeanne, 44			fax: (+32-2) 650.34.66
1050 Brussels
Belgium
====================================================================

I am one more reader who still does not understand the rationale
behind standardizing the average with the range for this problem:
Bob Wheeler (bwheeler,@,echip,.,com) wrote:
: My reading of this was that the problem was only partially
: statistical, as most real problems are. I suspect the "regular" 
: players object to an "occasional" player who by chance obtains 
: a very high score and thus wins a top spot. In such a case, dividing
: by the range helps.  Of course, without talking to Carolyn Longwoth,
In Carolyn's problem, there were people with 13 scores, on up to 
34 scores.  A SINGLE score at scrabble will not give a person the high
average; you cannot score 5000, say.  For 13 vs 34 scores, it seems
to me that the persons with 34 scores would tend to have the larger
personal ranges of scores, too, so that the adjustment that Bob
recommends would make the injustice WORSE, not better - for two
people with the same, rather-high score, the higher number would
come for the person with the smaller range, or, typically, the
shorter series....
I try to consider what happens if you look at Average/Max rather
than Average/Range, but that does not seem to improve fairness, 
either.  Am I overlooking something?
 (For the real problem, - as I suggested last time - give multiple
prizes.)
Rich Ulrich, biostatistician                wpilib+@pitt.edu
http://www.pitt.edu/~wpilib/index.html   Univ. of Pittsburgh

On Wed, 25 Jun 1997 21:33:38 -0800, bil2rowe@earthlink.net (Bill Rowe)
wrote:
>> nothing will be gained by using the median, although for
>> the simple purposes of the original poster, the median
>> divided by the range will no doubt work as well.
>
>No, this isn't right. The fact the median is a less efficient estimator of
>central tendency is precisely the reason it is the better choice. Being
>less efficient means the median is converges more slowly as observations
>are added, i.e., it is less sensitive to an extreme observation.
>
And what is wrong with extreme observations? If a player does
particularly well or particularly badly in a game, why shouldn't this
fact contribute to the player's ranking?
>Dividing the median by the range does add weight for consistent play. It
>also means a good player might rank lower as a result of one hot game than
>a consistent but poorer player. I doubt this would be considered
>acceptable for most people as a ranking system.
>
If a player has an off game now and then, they are therefore a weaker
player than if they were consistent. We might all prefer to be judged
at our best, but this does desire does not necessarily lead to a good
ranking system.
>If the total number of games is fairly large it is likely ranking
>according to median score will be the same as ranking by average score.
>For a small number of games there is a much better chance there will be a
>significant difference between the two methods.
--
Joe Otten, Sheffield, England, Europe.
Research Student and Green Party Policy Co-ordinator
joe.otten@virgin.net
http://freespace.virgin.net/joe.otten/
Opinions expressed are my own, and not necessarily those of the Green Party, 
Sheffield University, Virgin net, or anybody else in particular. However 
each of these organisations would be well advised to concur.

Jim Clark wrote:
> Are there standard general measures of the predictability of a
> sequence?
Spectrum analysis will give you the constituends. The more homogeneous
the spectrum, the less predictable the sequence. In the limit, with a
uniform spectrum, you have random (white) noise.
-- 
Motto: Think it through!  http://web.mit.edu/camoes/public/home.html

Charley Harp wrote:
> If by "background," however, you mean the mathematical basis for the simplex 
> (and more recent) methods for solving linear programs, I recommend that you 
> start with the classic text
> 
>    Hillier, Frederick S., and Lieberman, Gerald J., "Introduction to
>    Operations Research," McGraw-Hill, Inc., Sixth Edition, 1995.
Bertsimas and Tsitsikilis came up with a new book which I find great at
explaining carefully all the theoretical points. It's new from Athena
publishing, "Linear programming".
-- 
Motto: Think it through!  http://web.mit.edu/camoes/public/home.html

Petri S Vesa wrote:
> I'm analysing a data with SPSS and trying to do a regression 
> analysis. The dependent variable could get only some specific
> values (10, 30, 50, 100 etc.) and so I would like to use the 
> Tobit-model to achieve the best possible result.
Are these values ordinal or cardinal? In the former case you would
be better off using an order model, like ologit or oprobit. Tobit
is not designed for discrete LHS vars, just for a specific type of
error in measurement.
-- 
Motto: Think it through!  http://web.mit.edu/camoes/public/home.html

Brandewin wrote:
> 1) I collected my data from a relatively reliable source, but it seems to
> me that the  nature of it slightly changed over time. How can I check that
> my data are homogeneous over time, or, in other wors, how to identify a
> breakpoint?
Why not search for low-frequency effects with a Fourier transform? This
will then guide a model-based search for non-stationarity (you might
have smooth non-stationarities, I presume, rather than just a
discontinuous one - a breakpoint).
-- 
Motto: Think it through!  http://web.mit.edu/camoes/public/home.html

etjffr@zeus.ci.ua.pt wrote:
> Could any one tell me a real example of application of the
> law of the greater number's?
Law of large numbers (several of them): under several regularity conditions
the sample average of draws from a theoretical distribution converges in
probability to the expected value of the random variable characterized by
said distribution.
>  What's the pratical use in real life of this law?
It is the basis for a lot of proofs. And it is vastly misused by
practitioners, in what Huff called "the law of SMALL numbers".
-- 
Motto: Think it through!  http://web.mit.edu/camoes/public/home.html

<33AE88A3.798@ican.net> wrote:
> Can anybody please explain the differences between hazard functions and
> PROBIT/LOGIT? 
What are the similarities other that that they have a discrete observable?
Check any econometrics book. I recomend Amemiya: Advanced Econometrics, Harvard.
-- 
Motto: Think it through!  http://web.mit.edu/camoes/public/home.html

Jose Fernando Camoes Mendonca Oliveira Silva wrote:
> 
> Jim Clark wrote:
> 
> > Are there standard general measures of the predictability of a
> > sequence?
> 
> Spectrum analysis will give you the constituends. The more homogeneous
> the spectrum, the less predictable the sequence. In the limit, with a
> uniform spectrum, you have random (white) noise.
> 
> --
> Motto: Think it through!  http://web.mit.edu/camoes/public/home.html
Oh really? Doesn't a dirac pulse also have a uniform spectrum?
Paul de Wit
University of Twente
The Netherlands

Dan Bonnick wrote:
> 
> In article <33AA08EB.75F61B58@eos.ncsu.edu>, "Pavel E. Guarisma"
>  writes
> >ModTollens wrote:
> >>
> >> Such an interesting thought.  I think this allows me to ask the question,
> >> "Is life fair?"
> >> I am very interested in any response.
> >
> >Sure!
> >Life, in the long run, is fair!!
> 
> [apologies in advance for the near-crosspost]
> 
> What about the second law of thermodynamics?
> 
?????
> 
> I don't know about you, but I think my life is finite - there won't be
> enough time to get to the central limit...
> 
That's a shame!! I plan to live forever!!! ;)
In any case, in my own midnight stupor, what I meant to say was that, as
one lives his or her life, one expects (well, at least I expect!) the
good things to even out with the bad. This is to say, assuming I live a
full life (nothing nasty happens to me before I reach, say, 65) I hope
to lay in my death bed, look back on my life and say, "That was pretty
cool...". Sort of like having a mental list of pluses and minuses and
finding that, after a full (as previously defined) life, I have about
the same amount of pluses and minuses.
Hummm...I think I'm ranting again. And it's still not 11 pm!!
Take care,
-- 
DON'T THINK OF IT AS DYING, said Death. JUST THINK OF IT AS LEAVING
EARLY TO
AVOID THE RUSH.
         http://www4.ncsu.edu/eos/users/p/peguaris/WWW/
         *********************************************
         *            Pavel E. Guarisma N.           *
         *           peguaris@eos.ncsu.edu           *
         *                                           *
         *    Operations Research Graduate Program   *
         *      North Carolina State University      *
         *********************************************

Edoardo Maria Airoldi
Student at Bocconi University
Milan
I suggest you an article from Kintchine, "Giornale dell'Istituto
Italiano degli Attuari" 1935 "Sul dominio di attrazione della legge di
gauss".
Oppure, Levy, Calcul des Probabilites Paris 1925, but He states an only
sufficient condition, even if in his opinion it is necessary/sufficient
cond.
		Bye