Filling Area Under A Curve

0.1 Libraries

library(data.table)
library(ggplot2)

So this just shows a few ways to fill in the area under a curve using ggplot2.

1 Make a Distribution

First I’m going to make a normal distribution

normalDistribution <- data.frame(
    x = seq(-4,4, by = 0.01),
    y = dnorm(seq(-4,4, by = 0.01))
)

2 Two-tailed

Now define the critical values.

criticalValues <- qnorm(c(.025,.975))

shadeNormalTwoTailedLeft <- rbind(c(criticalValues[1],0), subset(normalDistribution, x < criticalValues[1]))

shadeNormalTwoTailedRight <- rbind(c(criticalValues[2],0), subset(normalDistribution, x > criticalValues[2]), c(3,0))

And make the plot.

ggplot(normalDistribution, aes(x,y)) +
    geom_line() +
    geom_polygon(data = shadeNormalTwoTailedLeft, aes(x=x, y=y, fill="red")) +
    geom_polygon(data = shadeNormalTwoTailedRight, aes(x=x, y=y, fill="red")) +
    guides(fill="none") +
    geom_hline(yintercept = 0) +
    geom_segment(aes(x = criticalValues[1], y = 0, xend = criticalValues[1], yend = dnorm(criticalValues[1]))) +
    geom_segment(aes(x = criticalValues[2], y = 0, xend = criticalValues[2], yend = dnorm(criticalValues[2]))) 

3 Right-tailed

criticalValue <- qnorm(.95)

shadeNormal <- rbind(c(criticalValue,0), subset(normalDistribution, x > criticalValue), c(3,0))

ggplot(normalDistribution, aes(x,y)) +
    geom_line() +
    geom_polygon(data = shadeNormal, aes(x=x, y=y, fill="red")) +
    guides(fill="none") +
    geom_hline(yintercept = 0) +
    geom_segment(aes(x = criticalValue, y = 0, xend = criticalValue, yend = dnorm(criticalValue))) 

4 Left-tailed

criticalValue <- qnorm(.15)

shadeNormal <- rbind(c(criticalValue,0), subset(normalDistribution, x < criticalValue))

ggplot(normalDistribution, aes(x,y)) +
    geom_polygon(data = shadeNormal, aes(x=x, y=y, fill="red")) +
    geom_line() +
    guides(fill="none") +
    geom_hline(yintercept = 0) +
    geom_segment(aes(x = criticalValue, y = 0, xend = criticalValue, yend = dnorm(criticalValue)))