Beta Binomial Distribution

Tags: #Math #Statistics

Equation

x∼f(x|n,α,β),f(x|n,α,β)=∫01Bin(x|n,p)Beta(p|α,β)dp,f(x|n,α,β)=CnxB(x+α,n−x+β)B(α,β)

Latex Code

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                                 x \sim f(x | n, \alpha, \beta), \\
f(x | n, \alpha, \beta) = \int_{0}^{1} \text{Bin}(x|n,p)\text{Beta}(p|\alpha,\beta) dp , \\
f(x | n, \alpha, \beta) = C^{x}_{n} \frac{B(x+\alpha, n -x + \beta)}{B(\alpha,\beta)}

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Introduction

Equation


x∼f(x|n,α,β) f(x|n,α,β)=∫01Bin(x|n,p)Beta(p|α,β)dp f(x|n,α,β)=CnxB(x+α,n−x+β)B(α,β)

Latex Code

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x \sim f(x | n, \alpha, \beta), \\
f(x | n, \alpha, \beta) = \int_{0}^{1} \text{Bin}(x|n,p)\text{Beta}(p|\alpha,\beta) dp , \\
f(x | n, \alpha, \beta) = C^{x}_{n} \frac{B(x+\alpha, n -x + \beta)}{B(\alpha,\beta)}

Explanation

Latex code for the Beta Binomial Distribution. Beta Binomial Distribution describe the situation that the probability of success in each trial is heteregenous or different as Beta(p|α,β).

  • Beta Binomial Distribution: x∼f(x|n,α,β)
  • Hyperparameters of α,β of beta distribution
  • Binomial trials Cnx

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