Posted by: Gary Ernest Davis on: March 26, 2013

My

After some data munging, I got unemployment data, 2000-2013, byÂ metropolitanÂ area, Â from theÂ BureauÂ of LaborÂ StatisticsÂ website into R.

From there, extracting subsets of the data isÂ straightforward. Here is theÂ histogramÂ – over U.S.Â metropolitanÂ areas – for 2000: and here are the basicÂ descriptiveÂ statistics:

Mean = 4.2

Standard deviation = 2.0

Skewness = 3.1

Kurtosis = 15.9

(An astute observer will notice that these are not R-producedÂ histograms, and they are not. I produced theÂ histogramsÂ in Mathematica, which I like much better for this purpose.)

This is a highly skewed (skewness = 3.1)Â and very peaky (15.9) distribution. By way of comparison a normal distribution has skewness 0 and kurtosis 3.

So, relying on experience and aÂ guess, IÂ transformedÂ the data by taking logs. Here is the resulting histogram andÂ descriptiveÂ statistics: Â Â

Mean = 1.4

Standard deviation = 0.4

Skewness = 1.1

Kurtosis = 5.4

Still we see that the log-transformed data is skewed and very peaky. So, on the principle that when you’re on a good thing stick to it, I transformed the data by once againÂ takingÂ logs. That is, the data entries are now the log of the log of theÂ originalÂ unemployment rates. Here’s theÂ histogramÂ andÂ descriptiveÂ statistics that result:

Mean = 0.28

Standard deviation = 0.26

Skewness = -0.09

Kurtosis = 4.04

This is an almostÂ symmetricÂ distributionÂ (skewness =Â -0.09) but it is still a little peakier than aÂ normalÂ distributionÂ (kurtosis =Â 4.04 compared with 3 for a normal distribution). So I am guessing that the log-log transformed data might be well-fitted by a normal-inverse Gaussian distribution.

I have never before seenÂ naturallyÂ occurringÂ data that mightÂ reasonablyÂ be Â described as log-log normal-inverse Gaussian.

I am wondering what theÂ distributionsÂ for the years 2001-2013 willÂ produce.

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