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| title | chunk | source | category | tags | date_saved | instance |
|---|---|---|---|---|---|---|
| Box–Cox distribution | 1/1 | https://en.wikipedia.org/wiki/Box–Cox_distribution | reference | science, encyclopedia | 2026-05-05T12:21:41.144483+00:00 | kb-cron |
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
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{\displaystyle f(y)={\frac {1}{\left[1-I(f<0)-\operatorname {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\}}
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 == Freeman, Jade; Reza Modarres. "Properties of the Power-Normal Distribution" (PDF). U.S. Environmental Protection Agency.