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beta_distribution [2023/01/19 15:37] daria |
beta_distribution [2023/01/20 12:32] daria |
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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] parametrized by two non-negative shape parameters, typically denoted by //alpha// and //beta//. | In probability theory and statistics, the Beta distribution is a family of continuous probability distributions defined on the interval [0,1] parametrized by two non-negative shape parameters, typically denoted by //alpha// and //beta//. | ||
- | f(x, | + | f(x, |
+ | |||
+ | where | ||
+ | //Beta// (The beta function), is a normalization constant to ensure that the total probability is 1 and has the formula | ||
- | where beta(z,w) = integral from 0 to 1 of t^(z-1)//(1-t)^(w-1) dt.// | + | Beta(alpha,beta) = //integral from 0 to 1 of t^(alpha-1)*(1-t)^(beta-1) dt.// |
- | support 0 <= x <= 1 | ||
^Parameter^Description | ^Parameter^Description | ||
- | |A |The first shape parameter |2.0 |A>0 | | + | |alpha |The first shape parameter |2.0 |alpha>0 | |
- | |B | + | |beta |The second shape parameter|2.0 |