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| | In [[statistics]], 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 |
| | |
| | :<math> |
| | f(y) = \frac{1}{\left(1-I(f<0)-\sgn(f)\Phi(0,m,\sqrt{s})\right)\sqrt{2 \pi s^2}} \exp\left\{-\frac{1}{2s^2}\left(\frac{y^f}{f} - m\right)^2\right\} |
| | </math> |
| | |
| | for ''y'' > 0, where ''m'' is the [[location parameter]] of the distribution, ''s'' is the dispersion, ''ƒ'' is the family parameter, ''I'' is the [[indicator function]], Φ is the [[cumulative distribution function]] of the [[standard normal distribution]], and sgn is the [[sign function]]. |
| | |
| | ==Special cases== |
| | * ''ƒ'' = 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 |
| | }} |
| | |
| | {{DEFAULTSORT:Box-Cox distribution}} |
| | {{ProbDistributions|continuous-semi-infinite}} |
| | [[Category:Continuous distributions]] |
| | [[Category:Probability distributions]] |
| | |
| | {{statistics-stub}} |
Revision as of 23:46, 22 March 2013
In statistics, 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
for y > 0, where m is the location parameter of the distribution, s is the dispersion, ƒ is the family parameter, I is the indicator function, Φ is the cumulative distribution function of the standard normal distribution, and sgn is the sign function.
Special cases
References
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