Encyclopedia > Beta distribution

  Article Content

Beta distribution

In probability theory and statistics, the beta distribution is a continuous probability distribution with the probability density function defined on the [0;1] interval:

<math> f(x) = \frac{x^{a-1}(1-x)^{b-1}}{\int_0^1 u^{a-1} (1-u)^{b-1}\, du} </math>

where a and b are parameters.

The special case of the beta distribution, when a = 1 and b = 1, is the standard uniform distribution.

The expected value and standard deviation of a beta random variable X with parameters a and b are given by the formulae:

<math> E(X) = \frac{a}{a+b} </math>
<math> Var(X) = \frac{ab}{(a+b)^2(a+b+1)} </math>



All Wikipedia text is available under the terms of the GNU Free Documentation License

 
  Search Encyclopedia

Search over one million articles, find something about almost anything!
 
 
  
  Featured Article
1904

... 7 - Ernst Ginsberg[?], actor and film director (+ 1964) February 11 - Henry LaBouisse[?], head of UNICEF (1965-1979) February 11 - Sir Keith Holyoake, New Zealand ...

 
 
 
This page was created in 34.3 ms