# Box–Cox distribution

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Box–Cox distribution

The Box–Cox distribution (also known as the power-normal distribution) is the distribution of a random variable "X" for which the Box–Cox transformation on "X" follows a truncated normal distribution. It is a continuous probability distribution having probability density function (pdf) given by

:$f\left(y\right) = frac\left\{1\right\}\left\{left\left(1-I\left(f<0\right)-sgn\left(f\right)Phi\left(0,m,sqrt\left\{s\right\}\right) ight\right)sqrt\left\{2 pi s^2 expleft\left\{-frac\left\{1\right\}\left\{2s^2\right\}left\left(frac\left\{y^f\right\}\left\{f\right\} - m ight\right)^2 ight\right\}$

for "y" > 0, where "m" is the location parameter of the distribution, "s" is the dispersion, "&fnof;" is the family parameter, "I" is the indicator function, &Phi; is the cumulative distribution function of the standard normal distribution, and sgn is the sign function.

pecial cases

* "&fnof;" = 1 gives a truncated normal distribution.

References

*cite paper
title = Properties of the Power-Normal Distribution
last = Freeman
coauthors = Reza Modarres
publisher = U.S. Environmental Protection Agency
url = http://www.udc.edu/docs/dc_water_resources/technical_reports/report_n_190.pdf

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