To install click the Add extension button. That's it.

The source code for the WIKI 2 extension is being checked by specialists of the Mozilla Foundation, Google, and Apple. You could also do it yourself at any point in time.

4,5
Kelly Slayton
Congratulations on this excellent venture… what a great idea!
Alexander Grigorievskiy
I use WIKI 2 every day and almost forgot how the original Wikipedia looks like.
Live Statistics
English Articles
Improved in 24 Hours
Added in 24 Hours
Languages
Recent
Show all languages
What we do. Every page goes through several hundred of perfecting techniques; in live mode. Quite the same Wikipedia. Just better.
.
Leo
Newton
Brights
Milds

Bates distribution

From Wikipedia, the free encyclopedia

Bates
Probability density function
BatesPDF.svg
Cumulative distribution function
BatesCDF.svg
Parameters
integer
Support
PDFsee below
Mean
Variance
Skewness0
Ex. kurtosis
CF

In probability and statistics, the Bates distribution, named after Grace Bates, is a probability distribution of the mean of a number of statistically independent uniformly distributed random variables on the unit interval.[1] This distribution is sometimes confused[2] with the Irwin–Hall distribution, which is the distribution of the sum (not the mean) of n independent random variables uniformly distributed from 0 to 1.

Definition

The Bates distribution is the continuous probability distribution of the mean, X, of n independent uniformly distributed random variables on the unit interval, Ui:

The equation defining the probability density function of a Bates distribution random variable X is

for x in the interval (0,1), and zero elsewhere. Here sgn(nxk) denotes the sign function:

More generally, the mean of n independent uniformly distributed random variables on the interval [a,b]

would have the probability density function (PDF) of

Therefore, the PDF of the distribution is

Extensions to the Bates distribution

Instead of dividing by n we can also use n to create a similar distribution with a constant variance (like unity). By subtracting the mean we can set the resulting mean to zero. This way the parameter n would become a purely shape-adjusting parameter, and we obtain a distribution which covers the uniform, the triangular and, in the limit, also the normal Gaussian distribution. By allowing also non-integer n a highly flexible distribution can be created (e.g. U(0,1) + 0.5U(0,1) gives a trapezodial distribution). Actually the Student-t distribution provides a natural extension of the normal Gaussian distribution for modeling of long tail data. And such generalized Bates distribution is doing so for short tail data (kurtosis < 3).

See also

Notes

  1. ^ Jonhson, N. L.; Kotz, S.; Balakrishnan (1995) Continuous Univariate Distributions, Volume 2, 2nd Edition, Wiley ISBN 0-471-58494-0(Section 26.9)
  2. ^ "The thing named "Irwin-Hall distribution" in d3.random is actually a Bates distribution · Issue #1647 · d3/d3". GitHub. Retrieved 2018-04-17.[permanent dead link]

References


This page was last edited on 4 June 2019, at 05:41
Basis of this page is in Wikipedia. Text is available under the CC BY-SA 3.0 Unported License. Non-text media are available under their specified licenses. Wikipedia® is a registered trademark of the Wikimedia Foundation, Inc. WIKI 2 is an independent company and has no affiliation with Wikimedia Foundation.