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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
In statistics, a power transform is a family of functions applied to create a monotonic transformation of data using power functions.It is a data transformation technique used to stabilize variance, make the data more normal distribution-like, improve the validity of measures of association (such as the Pearson correlation between variables), and for other data stabilization procedures.
The uniform distribution or rectangular distribution on [a,b], where all points in a finite interval are equally likely, is a special case of the four-parameter Beta distribution. The Irwin–Hall distribution is the distribution of the sum of n independent random variables, each of which having the uniform distribution on [0,1].
G. Gamma distribution; Gamma/Gompertz distribution; Gaussian q-distribution; Generalised hyperbolic distribution; Generalized beta distribution; Generalized chi-squared distribution
Wikipedia defines the Box-Cox distribution as “the distribution of a random variable X for which the Box–Cox transformation on X follows a truncated normal distribution.” The truncated-normal variate is defined as Y, which is the Box-Cox transformation of X: Y = (X^a – 1)/a if a is not equal to zero, else Y = ln(X).
The parameter q represents the degree of non-extensivity of the distribution. ... proposed by George Box and David Cox in 1964. [2] q-exponential
From a uniform distribution, we can transform to any distribution with an invertible cumulative distribution function. If G is an invertible cumulative distribution function, and U is a uniformly distributed random variable, then the random variable G −1 (U) has G as its cumulative distribution function.
Ban number-- Banach–Alaoglu theorem-- Banach algebra-- Banach algebra cohomology-- Banach bundle-- Banach bundle (non-commutative geometry)-- Banach fixed-point ...