Beta Binomial Distribution

Tags: #Math #Statistics

Equation

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

Latex Code

                                 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


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

Latex Code

            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 $$\text{Beta}(p|\alpha,\beta)$$.

  • Beta Binomial Distribution: $$x \sim f(x | n, \alpha, \beta)$$
  • Hyperparameters of $$\alpha,\beta$$ of beta distribution
  • Binomial trials $$C^{x}_{n}$$

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    If only I could pass this exam with flying colors.
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