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Journal of the Optical Society of America

Journal of the Optical Society of America

  • Vol. 58, Iss. 9 — Sep. 1, 1968
  • pp: 1267–1272

Permanence of the Log-Normal Distribution

R. L. MITCHELL  »View Author Affiliations


JOSA, Vol. 58, Issue 9, pp. 1267-1272 (1968)
http://dx.doi.org/10.1364/JOSA.58.001267


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Abstract

The distribution of the sum of log-normal variates is shown for most cases of interest to be very accurately represented by a log-normal distribution instead of a normal or Rayleigh distribution that might be expected from the central-limit theorem. As a result, observation of the log-normal distribution for the fluctuations of flux received after propagation through a random medium can be readily explained, regardless of the size of the receiving aperture. In every case, the log-normal distribution is a better representation than the normal for the distribution of the sum of log-normal variates. However, in some cases not even the log-normal distribution is very accurate. The questions of convergence and accuracy are examined in detail.

Citation
R. L. MITCHELL, "Permanence of the Log-Normal Distribution," J. Opt. Soc. Am. 58, 1267-1272 (1968)
http://www.opticsinfobase.org/josa/abstract.cfm?URI=josa-58-9-1267

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