What is the Bates Distribution?
The distribution was derived by Grace Bates (1955) for testing the null hypothesis that a particular distribution is uniform distribution, with the alternate hypothesis being that it is a truncated exponential distribution.
Shape of the Distribution
The distribution can resemble a bell curve; although the shape of the PDF is heavily dependent on how many items are in the sample— the shape can be triangular (for n = 2), uniform (for n = 1) or unimodal (for n > 2).
Standardized Bates Distribution
A standardized Bates distribution is commonly found in statistical software packages and has the following characteristics: mean = 0; standard deviation = 1; sample size = 12 (Kotz & Dorp, 2004).
An important historical use of the standardized Bates distribution was that it generated standard normal variables in computing.
For n = 1, the Bates is an exact match for a uniform distribution. For n = 2, it matches a triangular distribution.
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.
Kotz, S. & Dorp, J. (2004). Beyond Beta: Other Continuous Families of Distributions with Bounded Support and Applications. World Scientific.
Wolfram. Bates Distribution. Retrieved July 9, 2019 from: https://reference.wolfram.com/language/ref/BatesDistribution.html
Stephanie Glen. "Bates Distribution: Definition" From StatisticsHowTo.com: Elementary Statistics for the rest of us! https://www.statisticshowto.com/bates-distribution/
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