Beta distribution

\(\displaystyle x\in [0,1] \)일 때,

\(\Large \text{Beta}(\alpha, \beta) = f(x; \alpha, \beta) = \text{contant}\cdot x^{\alpha -1 }(1-x)^{\beta -1} \)

\(\Large = \frac{1}{\text{B}(\alpha, \beta)} x^{\alpha -1 }(1-x)^{\beta -1} \)

B is beta function. (여기서는 normalizer역할)

hyperparameter \(\alpha, \beta\)를 주었을 때 위의 pdf를 가지는 분포가 beta분포.

conjugate prior probability distribution for the

• Bernoulli,
• binomial,
• negative binomial,
• geometric distributions.