Part_B.qmd

---
title: "STA426_Week1_Ex2"
format: html
editor: visual
---

## Week1 - Part B

### Description:

*Create an HTML document with R code that samples 100 values from a negative binomial distribution (say, mu=10, dispersion=2; using the parameterisation with mean=mu and variance=mu+mu2 \*dispersion); create a histogram of sampled data on both the linear and log \[or maybe log(x+1) due to zeros\] scale; Write 1-2 sentences to describe your steps (ideally also with section headings) and report the mean and variance of the sample in line in the text.*

Load tidyverse for convenience and better plots.

```{r}
library(tidyverse)

```

Step 1: sample 100 values from a negative binomial distribution with the indicated parameters.

```{r}
set.seed(100) # for reproducibility
x <- rnbinom(n = 100, size = 2, # size is the dispersion parameter
        mu = 10)
```

Step 2: Create plots

```{r}
df <- data.frame(x) # turn it into a dataframe for ggplot

df %>%
  ggplot(aes(x = x)) +
  geom_histogram() +
  ggtitle("histogram - linear scale") +
  theme(plot.title = element_text(hjust = 0.5))

df %>%
  mutate(x = log(x + 1)) %>% # transform data
  ggplot(aes(x = x)) +
  geom_histogram() +
  ggtitle("histogram - log (x +1)") +
  theme(plot.title = element_text(hjust = 0.5))

```

Step 3: Report mean and variance.

Using the mean and variance functions we get a mean of

```{r}
#| echo: false
mean(x)
```

and a variance of

```{r}
#| echo: false
var(x)
```

\