Box–Cox distribution


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

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
first = Jade
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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