February 2013 Fully defined by mean and variance, asymmetrically bound  the charms of the lognormal distribution are quite clear. One of the goto distributions for curve fitting, it's regularly used to model common phenomena. Google 'lognormal electricity' for example and the first hit will explain that 'the log normal distribution was found to fit the historical [electricity market price] best'.
However until now I'd missed somehow the obvious  that the distribution's prevalence is easily explained by the extension of the Central Limit Theorem to the logdomain. So, whereas normals arise from the sum of many independent and identically distributed random variables ^{[1]}, lognormals arise as a product of the same variables ^{[2]}.
It's easy to imagine all kinds of process that are determined by the product of random variates, not just electricity prices. The financial Quants love this distribution because of their infatuation with compounded returns. Apparently also the latency periods of diseases follow a lognormal (obvious), the number of crystals in icecream (plausible), and the length of sentences in the works of George Bernard Shaw (incredible!).
Below is a brilliant physical demonstration of the process that leads to the lognormal distribution, contrasted with the normal [3]. On the left the position of the bearings are determined by a sum of random displacements and collectively form a normal distribution. Conversely, on the right the positions are defined by a product of random events and collectively form a lognormal. P.s. if you've forgotten the proof of the Central Limit Theorem a nice 'elementary, but slightly cumbersome proof' is provided by Wolfram.
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