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06_distributions.html
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<!DOCTYPE html>
<html lang="" xml:lang="">
<head>
<title>Univariate Probability Distributions</title>
<meta charset="utf-8" />
<meta name="author" content="Andrew MacDonald" />
<script src="assets/header-attrs-2.8/header-attrs.js"></script>
<link href="assets/remark-css-0.0.1/default.css" rel="stylesheet" />
<link href="assets/remark-css-0.0.1/hygge.css" rel="stylesheet" />
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<body>
<textarea id="source">
class: title-slide, middle
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# A Field Guide to the Univariate Distributions
<hr width="65%" align="left" size="0.3" color="orange"></hr>
## Introduction
<hr width="65%" align="left" size="0.3" color="orange" style="margin-bottom:40px;" alt="@Martin Sanchez"></hr>
.instructors[
**Biodiversity Modelling** - Andrew MacDonald
]
<img src="assets/img/bg.jpg" width="25%" style="margin-top:20px;"></img>
---
<div style='text-align:center;'>
<img src="assets/img/meme.jpg" width="400px"></img>
</div>
---
# Two flavours
--
### Discrete Distributions (integers, counts of things)
Described with a **probability mass function**
--
### Continuous distributions (not integers!)
Described with a **probability density function**
---
## Discrete distributions
$$
0 \leq [z] \leq 1
$$
--
$$
\sum [z] = 1
$$
---
## Continuous Distributions
$$
0 \leq [z]
$$
--
$$
\int_-^+[z]d[z] = 1
$$
---
## Moments
$$
\mu = \text{E}(z) = \sum z[z]
$$
---
$$
\sigma^2 = \text{E}((z-\mu)^2) = \sum (z - \mu)^2[z]
$$
class: inverse, middle, center
---
---
# The Binomial Distribution
<hr width="65%" size="0.3" color="orange" style="margin-top:-20px;"></hr>
---
class: inverse, middle, center
# The Binomial Distribution
<hr width="65%" size="0.3" color="orange" style="margin-top:-20px;"></hr>
---
.pull-left[
```r
curve(dbinom(x,
size = 20,
p = 0.2),
n = 21,
type = "p",
xlim = c(0,20))
```
Probability Mass Function is
$$
\text{Pr}(y = k) = {n \choose k} p^k(1-p)^{n-k}
$$
]
.pull-right[
<!-- -->
]
---
.pull-left[
```r
curve(dbinom(x,
size = 20,
p = 0.2),
n = 21,
type = "p",
xlim = c(0,20))
curve(dbinom(x,
size = 20,
p = 0.8),
n = 21,
type = "p",
col = "red", add = TRUE, pch = 16)
curve(dbinom(x,
size = 20,
p = 0.1),
n = 21,
type = "p",
col = "blue", add = TRUE, pch = 16)
```
Probability Mass Function is
$$
\text{Pr}(y = k) = {n \choose k} p^k(1-p)^{n-k}
$$
]
.pull-right[
<!-- -->
]
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