[Peace-discuss] Mean Streets (2) (David Sirota on Populism, too)

[E. Wayne Johnson]

The Italian mathematical economists made a tremendous contribution to 
the field of the study of distributions in statistics, and that 
contribution is seldom given its rightful position.  Perhaps it's 
because they were Fascists.  But whether or not one wants to be subject 
to their ideology, their statistical mathematics is quite robust and 
interesting.

Much of the inferential statistics that is done in the sciences assumes 
as a first principle that the data is normally distributed, and there is 
quite often a substantial artifice employed to invoke the central limit 
theorem and force the data into a Procrustean bed and torture the data 
until it confesses the original premise that prompted the study...

Laplace and Quetelet contributed much to the development of the familiar 
and symmetrical bell-shaped "Normal" curve with its skewness of Zero.

JC Kapetyn, an astronomer and mathematician, noted in 1903 that in 
Biology the distribution of populations is quite often skewed rather 
than "Normal", and proposed that the Underlying distribution was indeed 
"Gaussian Normal" but that a second distribution of events, or a series 
of unfortunate transforming events is at work that modifies the native 
normal distribution to a skewed distribution.  Kapetyn demonstrated how 
the log-normal distribution could result from such a "Kapetyn 
Transformation."  It is quite common in the design and analysis of 
experiments to get rid of skewness. But in the real world, it's the 
Skewness itself that is sometimes more interesting than inference from 
means because the skewness tells us about something that is happening to 
individuals.  All animals are created equal (normally distributed) but 
some are more equal than others (Kapetyn transformed and Orwellian 
Skewed). 

The Italian economist with the unlikely name of Luigi Amoroso recognized 
about 1910 or so that the series of unfortunate Poisson distributed 
events are described by Euler's gamma distribution, and if one plugs 
that back into the normal distribution as a Kapetyn Transformant, the 
significantly useful "Generalized Gamma Distribution" is the result.  
But Amoroso's work didnt get much traction in the Sir Ronald Fisher 
dominated field of inferences and normal distributed data, but the 
Generalized Gamma got rediscovered about 50 years later and is deeply 
related to the Negative Binomial distribution although the pedants will 
inform us that the one is discrete while the other is continuous as if 
there is some information transferred in such a declaration.  The 
neg-binomial is the distribution of the number of failures in a sequence 
of tries needed to get a specified number of successes, while the Gen 
Gamma tells us basically the same thing about errors and unfortunate 
events that occur along some cumulation of X.  And success can be 
fractional and messy.


In a parallel development in 1905, Max O. Lorenz published a paper 
called  /Methods of measuring the concentration of wealth,/
he details a method for graphical representation of the distribution of 
wealth by plotting the cumulative distribution function of wealth.
Perfect equality (uniform distribution) gives a straight line at 45 
degrees.  The Lorenz curve lies below the line of perfect equality.


In 1912, the Italian Corrado Gini offered a mathematical representation 
of the difference between the Lorenz curve and the
line of perfect equality.  This "Gini coefficient" has a wide range of 
applications in descriptive and inferential statistics.
Population biologist Christian Damgaard has recently (2000) developed a 
Lorenz Asymmetry Coefficient which is based on the shape of the Lorenz
curve that tends to point out where the wealth or stuff is concentrated.


Anthony Pomonis wrote:
>
> As "soft" as economic or political sciences /may/ /be,/ any move to 
> dismiss their insights/ /might be too casual. 
>
> http://en.wikipedia.org/wiki/Pareto_principle
>
> Thank you to all for a lively discourse...
>
>
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