test_file.Rmd

---
title: "Test doc"
author: "Corey Sparks"
date: "2/17/2022"
output: html_document
---

```{r setup, include=FALSE}
knitr::opts_chunk$set(echo = TRUE)
```

**Different distributions have different link functions....**

|   Distribution   | Mean    | Variance|  Link Function      | Range of Outcome |  
|:------------:|:----------------:|:----------------:|:----------------:|:----------------:|
|   Gaussian    | $\mu$ |$\sigma^2$ | Identity    | $-\infty ,  \infty$ |
|   Binomial  | $\pi$ | $n\pi(1-\pi)$ | $log \left (\frac{\pi}{1-\pi} \right )$    | $\frac{0,1,2,...n}{n}$ |
|   Poisson    | $\lambda$ | $\lambda$ | $log (\lambda)$    | $(0,1,2,...)$ |
|   Gamma    | $\mu$ | $\phi \mu^2$ | $log (\mu)$    | $(0, \infty)$ |
|   Negative Binomial | $n(1-p)/p$ | $n(1-p)/p^2$ | $log (\mu)$    | $(0,1,2,...)$ |
| Student-t | $\mu$ | $\frac{\sigma^2 \nu}{\nu-2}$| Identity | $-\infty ,  \infty$ |


$$
f(y) = 1/(2\sigma*sqrt(2* \pi))
$$

if
$$y= \mu = 1-exp(-(((x- \mu)/ \sigma)^2)/2))/(sqrt(2*\pi)*\sigma*((x-\mu)/\sigma)^2) if y!= \mu
$$