Kernel density estimation

In order to explain KDE, let us generate some one-dimensional data and build some histograms. Histograms are a good way to understand the underlying probability distribution of the data.

We can generate histograms using the following code block for reference:

> data <- rnorm(1000, mean=25, sd=5)
> data.1 <- rnorm(1000, mean=10, sd=2)
> data <- c(data, data.1)
> hist(data)
> hist(data, plot = FALSE)
$breaks
 [1]  0  5 10 15 20 25 30 35 40 45

$counts
[1]   8 489 531 130 361 324 134  22   1

$density
[1] 0.0008 0.0489 0.0531 0.0130 0.0361 0.0324 0.0134 0.0022 0.0001

$mids
[1]  2.5  7.5 12.5 17.5 22.5 27.5 32.5 37.5 42.5

$xname
[1] "data"

$equidist
[1] TRUE

attr(,"class")
[1] "histogram"

This code creates two artificial data-sets and combines them. Both datasets are based on the normal distribution; the first has a mean of 25 and standard deviation of 5, the second has a mean of 10 and standard deviation of 2. If we recall from basic statistics...