R: Histograms

hist {graphics}

R Documentation

Histograms

Description

The generic function hist computes a histogram of the given data values. If plot=TRUE, the resulting object of class "histogram" is plotted by plot.histogram, before it is returned.

Usage

hist(x, ...)

## Default S3 method:
hist(x, breaks = "Sturges", freq = NULL, probability = !freq,
     include.lowest = TRUE, right = TRUE,
     density = NULL, angle = 45, col = NULL, border = NULL,
     main = paste("Histogram of" , xname),
     xlim = range(breaks), ylim = NULL,
     xlab = xname, ylab,
     axes = TRUE, plot = TRUE, labels = FALSE,
     nclass = NULL, ...)

Arguments

x

a vector of values for which the histogram is desired.

breaks

one of:

a vector giving the breakpoints between histogram cells,
a single number giving the number of cells for the histogram,
a character string naming an algorithm to compute the number of cells (see Details),
a function to compute the number of cells.

In the last three cases the number is a suggestion only.

freq

logical; if TRUE, the histogram graphic is a representation of frequencies, the counts component of the result; if FALSE, relative frequencies (“probabilities”), component density, are plotted. Defaults to TRUE iff breaks are equidistant (and probability is not specified).

probability

an alias for !freq, for S compatibility.

include.lowest

logical; if TRUE, an x[i] equal to the breaks value will be included in the first (or last, for right = FALSE) bar. This will be ignored (with a warning) unless breaks is a vector.

right

logical; if TRUE, the histograms cells are right-closed (left open) intervals.

density

the density of shading lines, in lines per inch. The default value of NULL means that no shading lines are drawn. Non-positive values of density also inhibit the drawing of shading lines.

angle

the slope of shading lines, given as an angle in degrees (counter-clockwise).

col

a colour to be used to fill the bars. The default of NULL yields unfilled bars.

border

the color of the border around the bars. The default is to use the standard foreground color.

main, xlab, ylab

these arguments to title have useful defaults here.

xlim, ylim

the range of x and y values with sensible defaults. Note that xlim is not used to define the histogram (breaks), but only for plotting (when plot = TRUE).

axes

logical. If TRUE (default), axes are draw if the plot is drawn.

plot

logical. If TRUE (default), a histogram is plotted, otherwise a list of breaks and counts is returned.

labels

logical or character. Additionally draw labels on top of bars, if not FALSE; see plot.histogram.

nclass

numeric (integer). For S(-PLUS) compatibility only, nclass is equivalent to breaks for a scalar or character argument.

...

further graphical parameters to title and axis.

Details

The definition of “histogram” differs by source (with country-specific biases). R's default with equi-spaced breaks (also the default) is to plot the counts in the cells defined by breaks. Thus the height of a rectangle is proportional to the number of points falling into the cell, as is the area provided the breaks are equally-spaced.

The default with non-equi-spaced breaks is to give a plot of area one, in which the area of the rectangles is the fraction of the data points falling in the cells.

If right = TRUE (default), the histogram cells are intervals of the form (a, b], i.e., they include their right-hand endpoint, but not their left one, with the exception of the first cell when include.lowest is TRUE.

For right = FALSE, the intervals are of the form [a, b), and include.lowest really has the meaning of “include highest”.

A numerical tolerance of 10^{-7} times the median bin size is applied when counting entries on the edges of bins.

The default for breaks is "Sturges": see nclass.Sturges. Other names for which algorithms are supplied are "Scott" and "FD" / "Friedman-Diaconis" (with corresponding functions nclass.scott and nclass.FD). Case is ignored and partial matching is used. Alternatively, a function can be supplied which will compute the intended number of breaks as a function of x.

Value

an object of class "histogram" which is a list with components:

breaks

the n+1 cell boundaries (= breaks if that was a vector).

counts

n integers; for each cell, the number of x[] inside.

density

values \hat f(x_i), as estimated density values. If all(diff(breaks) == 1), they are the relative frequencies counts/n and in general satisfy \sum_i \hat f(x_i) (b_{i+1}-b_i) = 1, where b_i = breaks[i].

intensities

same as density. Deprecated, but retained for compatibility.

mids

the n cell midpoints.

xname

a character string with the actual x argument name.

equidist

logical, indicating if the distances between breaks are all the same.

Note

The resulting value does not depend on the values of the arguments freq (or probability) or plot. This is intentionally different from S.

Prior to R 1.7.0, the element breaks of the result was adjusted for numerical tolerances. The nominal values are now returned even though tolerances are still used when counting.

References

Becker, R. A., Chambers, J. M. and Wilks, A. R. (1988) The New S Language. Wadsworth \& Brooks/Cole.

Venables, W. N. and Ripley. B. D. (2002) Modern Applied Statistics with S. Springer.

Examples

op <- par(mfrow=c(2, 2))
hist(islands)
utils::str(hist(islands, col="gray", labels = TRUE))

hist(sqrt(islands), br = 12, col="lightblue", border="pink")
##-- For non-equidistant breaks, counts should NOT be graphed unscaled:
r <- hist(sqrt(islands), br = c(4*0:5, 10*3:5, 70, 100, 140), col='blue1')
text(r$mids, r$density, r$counts, adj=c(.5, -.5), col='blue3')
sapply(r[2:3], sum)
sum(r$density * diff(r$breaks)) # == 1
lines(r, lty = 3, border = "purple") # -> lines.histogram(*)
par(op)

utils::str(hist(islands, br=12, plot= FALSE)) #-> 10 (~= 12) breaks
utils::str(hist(islands, br=c(12,20,36,80,200,1000,17000), plot = FALSE))

hist(islands, br=c(12,20,36,80,200,1000,17000), freq = TRUE,
     main = "WRONG histogram") # and warning

[Package graphics version 2.0.0 ]