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In probability theory and statistics, the beta distribution is a family of continuous probability distributions defined on the interval [0, 1] or (0, 1) in terms of two positive parameters, denoted by alpha (α) and beta (β), that appear as exponents of the variable and its complement to 1, respectively, and control the shape of the distribution.
The beta family includes the beta of the first and second kind [7] (B1 and B2, where the B2 is also referred to as the Beta prime), which correspond to c = 0 and c = 1, respectively. Setting c = 0 {\displaystyle c=0} , b = 1 {\displaystyle b=1} yields the standard two-parameter beta distribution .
The Beta distribution on [0,1], a family of two-parameter distributions with one mode, of which the uniform distribution is a special case, and which is useful in estimating success probabilities. The four-parameter Beta distribution, a straight-forward generalization of the Beta distribution to arbitrary bounded intervals [,].
In statistics, the matrix variate beta distribution is a generalization of the beta distribution. If U {\displaystyle U} is a p × p {\displaystyle p\times p} positive definite matrix with a matrix variate beta distribution, and a , b > ( p − 1 ) / 2 {\displaystyle a,b>(p-1)/2} are real parameters, we write U ∼ B p ( a , b ) {\displaystyle ...
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Beta negative binomial distribution: The distribution of number of white balls observed until a fixed number black balls are observed. Dirichlet-multinomial distribution (also known as the multivariate Pólya distribution ): The distribution over the number of balls of each color, given n {\displaystyle n} draws from a Pólya urn where there ...
Beta regression is a form of regression which is used when the response variable, , takes values within (,) and can be assumed to follow a beta distribution. [1] It is generalisable to variables which takes values in the arbitrary open interval ( a , b ) {\displaystyle (a,b)} through transformations. [ 1 ]
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