---
output: html_document
---

### The Four-Parameter Beta Distribution $BETA(\alpha,\beta,c,d)$

- Suppose there exists a random variable $X \sim BETA(\alpha,\beta)\; X \in [0,1],\; \alpha,\beta >0$

- Now, suppose we wish to extend the support of $X$ outside $[0,1]$ to an arbitray interval.

- This can be accomplished by translating the distribution by $c \in \mathbb{R}$ and rescaling by $d > 0$.

- Applying the transformation $T = X \times d + c$, results in a new random variable $T \sim BETA(\alpha,\beta,c, d),\; T \in [c, c+d],\; \alpha,\beta,d >0$.  

- The random variable $T$ is said to follow the four-parameter Beta distribution
