# densityPlot

##### Nonparametric Density Estimates

`densityPlot`

contructs and graphs nonparametric density estimates, possibly conditioned on a factor, using the standard R `density`

function or by default `adaptiveKernel`

, which computes an adaptive kernel density estimate.
`depan`

provides the Epanechnikov kernel and `dbiwt`

provides the biweight kernel.

- Keywords
- hplot

##### Usage

`densityPlot(x, ...)`# S3 method for default
densityPlot(x, g, method=c("adaptive", "kernel"),
bw=if (method == "adaptive") bw.nrd0 else "SJ", adjust=1,
kernel, xlim, ylim,
normalize=FALSE, xlab=deparse(substitute(x)), ylab="Density", main="",
col=carPalette(), lty=seq_along(col), lwd=2, grid=TRUE,
legend=TRUE, show.bw=FALSE, rug=TRUE, ...)

# S3 method for formula
densityPlot(formula, data=NULL, subset,
na.action=NULL, xlab, ylab, main="", legend=TRUE, ...)

adaptiveKernel(x, kernel=dnorm, bw=bw.nrd0, adjust=1.0, n=500,
from, to, cut=3, na.rm=TRUE)
depan(x)
dbiwt(x)

##### Arguments

- x
a numeric variable, the density of which is estimated; for

`depan`

and`dbiwt`

, the argument of the kernel function.- g
an optional factor to divide the data.

- formula
an R model formula, of the form

`~ variable`

to estimate the unconditional density of`variable`

, or`variable ~ factor`

to estimate the density of`variable`

within each level of`factor`

.- data
an optional data frame containing the data.

- subset
an optional vector defining a subset of the data.

- na.action
a function to handle missing values; defaults to the value of the R

`na.action`

option, initially set to`na.omit`

.- method
either

`"adaptive"`

(the default) for an adaptive-kernel estimate or`"kernel"`

for a fixed-bandwidth kernel estimate.- bw
the geometric mean bandwidth for the adaptive-kernel or bandwidth of the kernel density estimate(s). Must be a numerical value or a function to compute the bandwidth (default

`bw.nrd0`

) for the adaptive kernel estimate; for the kernel estimate, may either the quoted name of a rule to compute the bandwidth, or a numeric value. If plotting by groups,`bw`

may be a vector of values, one for each group. See`density`

and`bw.SJ`

for details of the kernel estimator.- adjust
a multiplicative adjustment factor for the bandwidth; the default,

`1`

, indicates no adjustment; if plotting by groups,`adjust`

may be a vector of adjustment factors, one for each group. The default bandwidth-selection rule tends to give a value that's too large if the distribution is asymmetric or has multiple modes; try setting`adjust`

< 1, particularly for the adaptive-kernel estimator.- kernel
for

`densityPlot`

this is the name of the kernel function for the kernel estimator (the default is`"gaussian"`

, see`density`

); or a kernel function for the adaptive-kernel estimator (the default is`dnorm`

, producing the Gaussian kernel). For`adaptivekernel`

this is a kernel function, defaulting to`dnorm`

, which is the Gaussian kernel (standard-normal density).- xlim, ylim
axis limits; if missing, determined from the range of x-values at which the densities are estimated and the estimated densities.

- normalize
if

`TRUE`

(the default is`FALSE`

), the estimated densities are rescaled to integrate approximately to 1; particularly useful if the density is estimated over a restricted domain, as when`from`

or`to`

are specified.- xlab
label for the horizontal-axis; defaults to the name of the variable

`x`

.- ylab
label for the vertical axis; defaults to

`"Density"`

.- main
plot title; default is empty.

- col
vector of colors for the density estimate(s); defaults to the color

`carPalette`

.- lty
vector of line types for the density estimate(s); defaults to the successive integers, starting at 1.

- lwd
line width for the density estimate(s); defaults to 2.

- grid
if

`TRUE`

(the default), grid lines are drawn on the plot.- legend
a list of up to two named elements:

`location`

, for the legend when densities are plotted for several groups, defaults to`"upperright"`

(see`legend`

); and`title`

of the legend, which defaults to the name of the grouping factor. If`TRUE`

, the default, the default values are used; if`FALSE`

, the legend is suppressed.- n
number of equally spaced points at which the adaptive-kernel estimator is evaluated; the default is

`500`

.- from, to, cut
the range over which the density estimate is computed; the default, if missing, is

`min(x) - cut*bw, max(x) + cut*bw`

.- na.rm
remove missing values from

`x`

in computing the adaptive-kernel estimate? The default is`TRUE`

.- show.bw
if

`TRUE`

, show the bandwidth(s) in the horizontal-axis label or (for multiple groups) the legend; the default is`FALSE`

.- rug
if

`TRUE`

(the default), draw a rug plot (one-dimentional scatterplot) at the bottom of the density estimate.- …
arguments to be passed down.

##### Details

If you use a different kernel function than the default `dnorm`

that has a
standard deviation different from 1 along with an automatic rule
like the default function `bw.nrd0`

, you can attach an attribute to the kernel
function named `"scale"`

that gives its standard deviation. This is true for
the two supplied kernels, `depan`

and `dbiwt`

##### Value

`densityPlot`

invisibly returns the `"density"`

object computed (or list of `"density"`

objects) and draws a graph.
`adaptiveKernel`

returns an object of class `"density"`

(see `density)`

.

##### References

Fox, J. and Weisberg, S. (2019)
*An R Companion to Applied Regression*, Third Edition, Sage.

W. N. Venables and B. D. Ripley (2002) *Modern Applied Statistics with S*. New York: Springer.

B.W. Silverman (1986) *Density Estimation for Statistics and Data Analysis*. London: Chapman and Hall.

##### See Also

##### Examples

```
# NOT RUN {
densityPlot(~ income, show.bw=TRUE, method="kernel", data=Prestige)
densityPlot(~ income, show.bw=TRUE, data=Prestige)
densityPlot(~ income, from=0, normalize=TRUE, show.bw=TRUE, data=Prestige)
densityPlot(income ~ type, data=Prestige)
densityPlot(~ income, show.bw=TRUE, method="kernel", data=Prestige)
densityPlot(~ income, show.bw=TRUE, data=Prestige)
densityPlot(~ income, from=0, normalize=TRUE, show.bw=TRUE, data=Prestige)
densityPlot(income ~ type, kernel=depan, data=Prestige)
densityPlot(income ~ type, kernel=depan, legend=list(location="top"), data=Prestige)
plot(adaptiveKernel(UN$infantMortality, from=0, adjust=0.75), col="magenta")
lines(density(na.omit(UN$infantMortality), from=0, adjust=0.75), col="blue")
rug(UN$infantMortality, col="cyan")
legend("topright", col=c("magenta", "blue"), lty=1,
legend=c("adaptive kernel", "kernel"), inset=0.02)
plot(adaptiveKernel(UN$infantMortality, from=0, adjust=0.75), col="magenta")
lines(density(na.omit(UN$infantMortality), from=0, adjust=0.75), col="blue")
rug(UN$infantMortality, col="cyan")
legend("topright", col=c("magenta", "blue"), lty=1,
legend=c("adaptive kernel", "kernel"), inset=0.02)
# }
```

*Documentation reproduced from package car, version 3.0-9, License: GPL (>= 2)*