Beta Distribution
A general type of statistical Distribution which is related to the Gamma Distribution. Beta distributions havetwo free parameters, which are labeled according to one of two notational conventions. The usual definition calls these
and 
, and the other uses 
and 
(Beyer 1987, p. 534). Theabove plots are for 
[solid], (1, 2) [dotted], and (2, 3) [dashed]. The probability function 
and Distribution Function 
are given by
 |  |  | |
|  | (1) | |
 | |  | (2) |
where
is the Beta Function, 
is the Regularized Beta Function, and
where , 
. The distribution is normalized since | |  | (3) |
|  | (4) |
The Characteristic Function is
 | (5) |
 | (6) |
 | |  | |
|  | ||
|  | (7) |
and the Variance, Skewness, and Kurtosis are
 | |  | (8) |
 | |  | (9) |
 | |  | |
| (10) |
The Mode of a variate distributed as
is  | (11) |
In ``normal'' form, the distribution is written
 | (12) |
| |  | (13) |
| |  | (14) |
| |  | (15) |
| |  | |
| (16) |
See also Gamma Distribution
References
Abramowitz, M. and Stegun, C. A. (Eds.). Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, 9th printing. New York: Dover, pp. 944-945, 1972. Beyer, W. H. CRC Standard Mathematical Tables, 28th ed. Boca Raton, FL: CRC Press, pp. 534-535, 1987.
- Mystic Pentagram
- Méiré Pattern
- Ménage Number
- Ménage Problem
- Möbius Band
- Möbius Function
- Möbius Group
- Möbius Inversion Formula
- Möbius Periodic Function
- Möbius Problem
- Möbius Shorts
- Möbius Strip
- Möbius Transformation
- Möbius Triangles
- Müller-Lyer Illusion
- Müntz Space
- Müntz's Theorem
- N
- Nabla
- Nagel Point
- Naive Set Theory
- Napierian Logarithm
- Napier's Analogies
- Napier's Bones
- Napier's Constant