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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

$f(y)=\frac{1}{(1-I(f<0)-\mathrm{sgn}(f)\mathrm{\Phi }(0,m,\sqrt{s}))\sqrt{2\pi s^2}}\exp \{-\frac{1}{2s^2}{(\frac{y^f}{f}-m)}^2\}$

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

• Template:Cite paper

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