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
In probability and statistics, the truncated normal distribution is the probability distribution derived from that of a normally distributed random variable by bounding the random variable from either below or above (or both). The truncated no ...
. It is a continuous
probability distribution having
probability density function
In probability theory, a probability density function (PDF), or density of a continuous random variable, is a function whose value at any given sample (or point) in the sample space (the set of possible values taken by the random variable) ca ...
(pdf) given by
:
for ''y'' > 0, where ''m'' is the
location parameter
In geography, location or place are used to denote a region (point, line, or area) on Earth's surface or elsewhere. The term ''location'' generally implies a higher degree of certainty than ''place'', the latter often indicating an entity with an ...
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
In probability and statistics, the truncated normal distribution is the probability distribution derived from that of a normally distributed random variable by bounding the random variable from either below or above (or both). The truncated no ...
.
References
*
Continuous distributions
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