Box–Cox distribution
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 ) = 1 [ 1 − I ( f < 0 ) − sgn ( f ) Φ ( 0 , m , s ) ] 2 π s 2 exp { − 1 2 s 2 ( y f f − m ) 2 } {\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.