Distributions of data: Gaussian, power-law, exponential, Pareto, Poisson, and barbell

Regular readers of this blog understand, or at least have heard of, distributions of data that look like a bell. Many toward the middle hump; tails of less frequent amounts on either end. Invoice amounts for large law departments follow that pattern, for example. Some readers might even speak comfortably about standard deviations (See my post of March 12, 2009: bell curves with 8 references.).

Along with normal, bell-curves there exist many other mathematical distributions of data, several of which this blog has covered. Legal managers who aspire to sophisticated data analysis should familiarize themselves with these ways to describe and understand data.

For example, a power-law distribution has a dominant number, a significant drop off to the next number, a lesser drop to the third, and on down to the proverbial long tail (See my post of April 27, 2010: power-law distributions with 6 references.).

Another distribution, referred to as exponential, looks like a hockey stick when graphed (See my post of Feb. 23, 2008: hockey-stick distribution of resolution times for lawsuits.). Still another variation goes by the name of the Italian economist, Vilifredo Pareto (See my post of May 21, 2008: the so-called 80-20 rule with 9 references.).

Poisson distributions, named after a French mathematician, describes another regular variation (See my post of Jan. 20, 2006: one of many kinds of numeric distributions; Aug. 16, 2006: predicts likelihood of event during a given time period; June 15, 2009: relation to queuing theory; and Dec. 28, 2010: Poisson distributions.). Sometimes the pattern of numbers bulges at either end (See my post of March 6, 2009: barbell of write-off percentages from poll.).

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