--- title: "The 'kde1d' package" author: "Stéphane Laurent" date: '2020-10-15' tags: R, statistics rbloggers: yes output: md_document: variant: markdown preserve_yaml: true html_document: highlight: kate keep_md: no highlighter: pandoc-solarized --- ```{r setup, include=FALSE} knitr::opts_chunk\$set(echo = TRUE, collapse = TRUE, fig.path="./figures/kde1d-") ``` 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: ```{r} 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: ```{r, fig.width=6, fig.height=3} 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: ```{r} print(dkde1d(max(y)+1, fit)) ``` The corresponding cumulative distribution function: ```{r, fig.width=6, fig.height=4} 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): ```{r, fig.width=6, fig.height=3} 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: ```{r, fig.width=6, fig.height=3} 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) ```