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