Bates distribution
Probability density function File:No image available | |||
Cumulative distribution function File:No image available | |||
Parameters |
integer | ||
---|---|---|---|
Support | |||
Mean | |||
Variance | |||
Skewness | 0 | ||
Excess kurtosis | |||
CF |
In probability and statistics, the Bates distribution, 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 with the Irwin–Hall distribution, which is the distribution of the sum (not 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(x − k) 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 of
The topic of this article may not meet Wikipedia's general notability guideline. (June 2011) |
This article includes a list of general references, but it lacks sufficient corresponding inline citations. (June 2011) |
Notes
- ^ Jonhson, N.L.; Kotz, S.; Balakrishnan (1995) Continuous Univariate Distributions, Volume 2, 2nd Edition, Wiley ISBN 0-471-58494-0(Section 26.9)
References
- Bates,G.E. (1955) "Joint distributions of time intervals for the occurrence of successive accidents in a generalized Polya urn scheme", Annals of Mathematical Statistics, 26, 705–720