# The ‘kde1d’ package

**Saturn Elephant**, and kindly contributed to R-bloggers]. (You can report issue about the content on this page here)

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It seems to me that the `kde1d`

package (One-Dimensional
Kernel Density Estimation) is not very known. I’ve never heard of it on
Stack Overflow, except in an answer of mine.

However this is a great package, IMHO. I’m going to show why I like it.

### The `d/p/q/r`

family

Estimating a density with the `kde1d`

function returns a
`kde1d`

object, and this makes available the density, the
distribution function, the quantile function associated to the density
estimate, as well as a sampler from the estimated distribution.

Let’s fit a density with `kde1d`

to a simulated Gaussian
sample:

library(kde1d) set.seed(666) y <- rnorm(100) fit <- kde1d(y)

Here is the density estimate, in green, along with the true density, in blue:

opar <- par(mar = c(3, 1, 1, 1)) plot(NULL, xlim = c(-3.5, 3.5), ylim = c(0, 0.4), axes = FALSE, xlab = NA) axis(1, at = seq(-3, 3, by=1)) curve(dkde1d(x, fit), n = 300, add = TRUE, col = "green", lwd = 2) curve(dnorm(x), n = 300, add = TRUE, col = "blue", lwd = 2)

The density can even be evaluated outside the range of the data:

print(dkde1d(max(y)+1, fit)) ## [1] 0.001684873

The corresponding cumulative distribution function:

opar <- par(mar = c(4.5, 5, 1, 1)) plot(NULL, xlim = c(-3.5, 3.5), ylim = c(0, 1), axes = FALSE, xlab = "x", ylab = expression("Pr("<="x)")) axis(1, at = seq(-3, 3, by=1)) axis(2, at = seq(0, 1, by=0.25)) curve(pkde1d(x, fit), n = 300, add = TRUE, col = "green", lwd = 2) curve(pnorm(x), n = 300, add = TRUE, col = "blue", lwd = 2)

The corresponding inverse cumulative distribution function is evaluated
by `qkde1d`

, and `rkde1d`

simulates from the
estimated distribution.

### Bounded data

By default, the data supplied to the `kde1d`

function is
assumed to be unbounded. For bounded data, use the
`xmin`

and/or `xmax`

options.

### Estimating monotonic densities

Now, something I use to convince my folks that `kde1d`

is
great. Consider a distribution having a monotonic density. The base
function `density`

does not correctly estimate the density
(at least, with the default settings):

set.seed(666) y <- rbeta(100, 1, 4) opar <- par(mar = c(3, 1, 1, 1)) plot(NULL, xlim = c(0, 1), ylim = c(0, 4), axes = FALSE, xlab = NA) axis(1, at = seq(0, 1, by=0.2)) lines(density(y, from = 0, to = 1), col = "green", lwd = 2) curve(dbeta(x, 1, 4), n = 300, add = TRUE, col = "blue", lwd = 2)

The monotonic aspect of the density does not occur in the estimated
density. With `kde1d`

, it does:

fit <- kde1d(y, xmin = 0, xmax = 1) opar <- par(mar = c(3, 1, 1, 1)) plot(NULL, xlim = c(0, 1), ylim = c(0, 4), axes = FALSE, xlab = NA) axis(1, at = seq(0, 1, by=0.2)) curve(dkde1d(x, fit), n = 300, add = TRUE, col = "green", lwd = 2) curve(dbeta(x, 1, 4), n = 300, add = TRUE, col = "blue", lwd = 2)

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**Saturn Elephant**.

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