Box–Cox distribution

Box–Cox distribution

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) = frac{1}{left(1-I(f<0)-sgn(f)Phi(0,m,sqrt{s}) ight)sqrt{2 pi s^2 expleft{-frac{1}{2s^2}left(frac{y^f}{f} - m ight)^2 ight}

for "y" > 0, where "m" is the location parameter of the distribution, "s" is the dispersion, "&fnof;" is the family parameter, "I" is the indicator function, &Phi; is the cumulative distribution function of the standard normal distribution, and sgn is the sign function.

pecial cases

* "&fnof;" = 1 gives a truncated normal distribution.

References

*cite paper
title = Properties of the Power-Normal Distribution
last = Freeman
first = Jade
coauthors = Reza Modarres
publisher = U.S. Environmental Protection Agency
url = http://www.udc.edu/docs/dc_water_resources/technical_reports/report_n_190.pdf


Wikimedia Foundation. 2010.

Игры ⚽ Нужен реферат?

Look at other dictionaries:

  • Multivariate normal distribution — MVN redirects here. For the airport with that IATA code, see Mount Vernon Airport. Probability density function Many samples from a multivariate (bivariate) Gaussian distribution centered at (1,3) with a standard deviation of 3 in roughly the… …   Wikipedia

  • Linux distribution — A Linux distribution is a member of the family of Unix like operating systems built on top of the Linux kernel. Such distributions (often called distros for short) are operating systems including a large collection of software applications such… …   Wikipedia

  • Les plus gros échecs du box-office américain — Liste des plus gros échecs du box office américain Article principal : Box office. Cette liste des plus gros échecs du box office américain répertorie les films américains dont les recettes n ont pas couvert les coûts de production et de… …   Wikipédia en Français

  • Liste Des Plus Gros Échecs Du Box-Office Américain — Article principal : Box office. Cette liste des plus gros échecs du box office américain répertorie les films américains dont les recettes n ont pas couvert les coûts de production et de distribution. Sommaire 1 Financement d un tournage 2… …   Wikipédia en Français

  • Liste des plus gros echecs du box-office americain — Liste des plus gros échecs du box office américain Article principal : Box office. Cette liste des plus gros échecs du box office américain répertorie les films américains dont les recettes n ont pas couvert les coûts de production et de… …   Wikipédia en Français

  • Liste des plus gros échecs du box-office américain — Article principal : Box office. Cette liste des plus gros échecs du box office américain répertorie les films américains dont les recettes n ont pas couvert les coûts de production et de distribution. Sommaire 1 Financement d un tournage 2… …   Wikipédia en Français

  • List of statistics topics — Please add any Wikipedia articles related to statistics that are not already on this list.The Related changes link in the margin of this page (below search) leads to a list of the most recent changes to the articles listed below. To see the most… …   Wikipedia

  • Power transform — In statistics, the power transform is a family of transformations that map data from one space to another using power functions. This is a useful data (pre)processing technique used to reduce data variation, make the data more normal distribution …   Wikipedia

  • List of mathematics articles (B) — NOTOC B B spline B* algebra B* search algorithm B,C,K,W system BA model Ba space Babuška Lax Milgram theorem Baby Monster group Baby step giant step Babylonian mathematics Babylonian numerals Bach tensor Bach s algorithm Bachmann–Howard ordinal… …   Wikipedia

  • Data transformation (statistics) — A scatterplot in which the areas of the sovereign states and dependent territories in the world are plotted on the vertical axis against their populations on the horizontal axis. The upper plot uses raw data. In the lower plot, both the area and… …   Wikipedia

Share the article and excerpts

Direct link
… Do a right-click on the link above
and select “Copy Link”