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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.
Box used the aphorism again in 1979, where he expanded on the idea by discussing how models serve as useful approximations, despite failing to perfectly describe empirical phenomena. [7] He reiterated this sentiment in his later works , where he discussed how models should be judged based on their utility rather than their absolute correctness.
However, when both negative and positive values are observed, it is sometimes common to begin by adding a constant to all values, producing a set of non-negative data to which any power transformation can be applied. [3] A common situation where a data transformation is applied is when a value of interest ranges over several orders of magnitude ...
Also, Y is undefined when X < 0, and hence Y must also be non-negative by dint of the Box-Cox transformation. The non-negativity enforced on Y forces fy(Y) to be NOT a Gaussian as one would have hoped, but a truncated Gaussian with truncation at Y = 0 and keeping only the part of the Y domain that is either greater than or less than zero.
George Edward Pelham Box FRS [1] (18 October 1919 – 28 March 2013) was a British statistician, who worked in the areas of quality control, time-series analysis, design of experiments, and Bayesian inference. He has been called "one of the great statistical minds of the 20th century".
An admissible model must be consistent with all the data points. Thus, a straight line (height i = b 0 + b 1 age i ) cannot be admissible for a model of the data—unless it exactly fits all the data points, i.e. all the data points lie perfectly on the line.
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