# Visualizing Sampling Distributions in ggplot2: Adding area under the curve

Thank you ggplot2tutor for solving one of my struggles. Apparently this is all it takes:

``````ggplot(NULL, aes(x = c(-3, 3))) +
stat_function(fun = dnorm, geom = "line")``````

I can’t begin to count how often I have wanted to visualize a (normal) distribution in a plot. For instance to show how my sample differs from expectations, or to highlight the skewness of the scores on a particular variable. I wish I’d known earlier that I could just add one simple geom to my ggplot!

Want a different mean and standard deviation, just add a list to the args argument:

```ggplot(NULL, aes(x = c(0, 20))) +
stat_function(fun = dnorm,
geom = "area",
args = list(
mean = 10,
sd = 3
))
```

Need a different distribution? Just pass a different distribution function to stat_function. For instance, an F-distribution, with the df function:

```ggplot(NULL, aes(x = c(0, 5))) +
stat_function(fun = df,
geom = "area",
args = list(
df1 = 2,
df2 = 10
))
```

You can make it is complex as you want. The original ggplot2tutor blog provides this example:

```ggplot(NULL, aes(x = c(-3, 5))) +
stat_function(
fun = dnorm,
geom = "area",
fill = "steelblue",
alpha = .3
) +
stat_function(
fun = dnorm,
geom = "area",
fill = "steelblue",
xlim = c(qnorm(.95), 4)
) +
stat_function(
fun = dnorm,
geom = "line",
linetype = 2,
fill = "steelblue",
alpha = .5,
args = list(
mean = 2
)
) +
labs(
title = "Type I Error",
x = "z-score",
y = "Density"
) +
scale_x_continuous(limits = c(-3, 5))
```

Have a look at the original blog here: https://ggplot2tutor.com/sampling_distribution/sampling_distribution/