Box–Cox distribution

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

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.