densities.Rmd

---
title: "Plotting Densities"
author: "Douglas Bates"
date: "2014-11-12"
output:
  ioslides_presentation:
    fig_caption: yes
    fig_retina: null
    keep_md: yes
    smaller: yes
    widescreen: yes
---
```{r preliminaries,echo=FALSE,results='hide'}
library(ggplot2)
options(show.signif.stars=FALSE)
```

# Evaluating densities<a id="sec-1"></a>

## Functions to evaluate densities<a id="sec-1-1"></a>

-   Functions to evaluate probability densities in R have names of the
    form `d<dabb>` where `dabb` is the abbreviated distribution name.  For
    example, `norm` for the normal (or Gaussian) density, `unif` for the
    uniform density, `exp` for the exponential density.  A more complete
    list of distributions and their abbreviations is given 
    [here](http://blog.revolutionanalytics.com/2010/08/distributions-in-r.html).

-   One simple way of plotting a theoretical density function is to
    establish a range of x values, evaluate the density (or probability
    mass function) on these values and plot the result.

## Determining the range of x values<a id="sec-1-2"></a>

-   It is not always straightforward to decide what a reasonable range of
    x values would be.  For example, if I want to plot the exponential
    density for the rate, $\lambda=0.2$, how far out on the right-hand tail
    should I go?  One way to answer this is to find, say, the 0.995
    quantile.
```{r expmax}
(xmax <- qexp(0.995, rate=0.2))
```
    and choose equally spaced values from 0, below which the density is zero, to `xmax`
```{r xvals}
xvals <- seq(0, xmax, length=100)
```


## Creating a plot<a id="sec-1-3"></a>
```{r densplot,fig.align='center'}
qplot(xvals, dexp(xvals, rate=0.2), geom="line", ylab="density", xlab="x")
```