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Topic: log normal?
Replies: 9   Last Post: Jan 1, 2013 6:17 AM

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Jim Burns

Posts: 1,200
Registered: 12/6/04
Re: log normal?
Posted: Dec 27, 2012 8:11 AM
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RichD wrote:
> Ocasionally I come across somethign called log
> normal, and I wonder, what is the purpose?
> The normal distribution is natural, but the log of that,
> seems unnatural, and unintuitive.
> Can anyone elaborate on its use?


In biology, variables whose logarithms tend to have a normal
distribution include:
Measures of size of living tissue (length, skin area, weight);[8]
The length of inert appendages (hair, claws, nails, teeth) of
biological specimens, in the direction of growth;[citation needed]
Certain physiological measurements, such as blood pressure of
adult humans (after separation on male/female subpopulations)[9]

Fitted cumulative log-normal distribution to annually maximum 1-day
rainfalls, see distribution fitting

Consequently, reference ranges for measurements in healthy
individuals are more accurately estimated by assuming a log-normal
distribution than by assuming a symmetric distribution about the mean.

In hydrology, the log-normal distribution is used to analyze
extreme values of such variables as monthly and annual maximum values of
daily rainfall and river discharge volumes.[10]
The image on the right illustrates an example of fitting the
log-normal distribution to ranked annually maximum one-day rainfalls
showing also the 90% confidence belt based on the binomial distribution.
The rainfall data are represented by plotting positions as part of a
cumulative frequency analysis.

In economics, there is evidence that the income of 97%?99% of the
population is distributed log-normally.[11]

In finance, in particular the Black?Scholes model, changes in the
logarithm of exchange rates, price indices, and stock market indices are
assumed normal[12] (these variables behave like compound interest, not
like simple interest, and so are multiplicative). However, some
mathematicians such as Benoît Mandelbrot have argued[citation needed]
that log-Levy distributions which possesses heavy tails would be a more
appropriate model, in particular for the analysis for stock market
crashes. Indeed stock price distributions typically exhibit a fat tail.[13]

The distribution of city sizes is lognormal. This follows from
Gibrat's law of proportionate (or scale-free) growth. Irrespective of
their size, all cities follow the same stochastic growth process. As a
result, the logarithm of city size is normally distributed. There is
also evidence of lognormality in the firm size distribution and of
Gibrat's law.

In reliability analysis, the lognormal distribution is often used
to model times to repair a maintainable system.

In wireless communication, "the local-mean power expressed in
logarithmic values, such as dB or neper, has a normal (i.e., Gaussian)
distribution." [14]

It has been proposed that coefficients of friction and wear may be
treated as having a lognormal distribution [15]


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