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Re: [POSSIBLE SPAM] The 'Brookhavenato r':
Self-organizi
Folks -- It is well to remember that all probability density
functions are mere tools for analyzing data. Nothing in nature
is either random or orderly. These are windows we peek out
from. In biology in particular the Normal mean is taken as the
'fact' about any population. In that field, studying the only
realm where Nature has produced functional individuality, individuals
are reckoned to be of no account. Science so far cannot deal
with individuals except insofar as one individual might be scanned
many times using many different probes, delivering population
data.
STAN
from Lewis L. Smith
The sender is a semiretired energy economist who came into economics
from finance and into complexity from economics and the securities
markets. Since 1994, he has been a pro bonum researcher in the
application of complexity to economics, with six papers and one
collaboration to his credit.
Long before there was a controversy over power laws, there was one
over the Gaussian or "normal" Distribution [ the famous
"bell shaped curve" ] which was derived from the heights of
French soldiers in 18th century. For roughly two hundred years, many
analysts thought that it was the universal descriptor of random events
and of the random aspects of nonrandom events, such as are the heights
of French soldiers, exclusive of their end points. Indeed for some
four decades in securities markets, it was devoutly believed that each
major market was driven by its own random process and that its
outputs, at least in terms of period-to-period log returns, could be
described by the normal curve.
[ If you didn't believe this, you were in danger of be
"excommunicated" from the academic division of the finance
community or at the very least, of being denied tenure. ]
In the last decade a vast literature has arisen disputing this
"article of faith" without settling on an alternative for
securities markets, or even settling the question of whether one
should use one, two or three distributions to characterize a given
market.
[ Say separate distributions for each tail and one other for the bulk
of the events ! See especially the writings of Didier Sornette
and Benoit Mandelbrot, among others. Also my paper for the June 2008
Oxford Conference on Business and Economics, "Do random series
exist ?". ]
My own awakening came when I went to work for an electric utility and
discovered that the expected lives of wooden poles are described by
the Poisson Distribution, and reinforced later on, when I headed a
study of sites for wind farms in which wind speed at a given height
and location was described by the Wiebull Distribution. And now,
in the course or revisiting econometrics for assorted reasons, I
realize that as a result of the current proliferation of estimators,
econometricians are stumbling upon all kinds of weird distributions,
some of which don't even have "official" names as yet,
situations in which are old friends, the chi-square and the t
distributions are not much help.
In particular, people who analyze stock markets and bioelectric series
often have problems in classifying a given run of data as conforming
to a log-normal distribution or a power law one. So the fact that a
distribution has turned up which seems to be the product of the two,
doesn't surprise me in the least.
So those who would like to find power laws in biology should be
forewarned >
[1] It aint going to be easy !
[2] The presence of power laws may NOT be in
one-to-one correspondence with some phenomenon of interest, and
such presence may not be restricted to a coherent group of phenomena,
so the presence or absence of a power law distribution in the data
cannot always be taken as "the signature" of a particular
phenomenon, of a class of phenomena or of a particular type of dynamic
behavior.
Cordially. ###
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