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## 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, warn.unused = TRUE, ...)

### Arguments

 x a vector of values for which the histogram is desired. breaks one of: a vector giving the breakpoints between histogram cells, a function to compute the vector of breakpoints, 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; the breakpoints will be set to pretty values. If breaks is a function, the x vector is supplied to it as the only argument. freq logical; if TRUE, the histogram graphic is a representation of frequencies, the counts component of the result; if FALSE, probability densities, component density, are plotted (so that the histogram has a total area of one). Defaults to TRUE if and only if 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 histogram 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. In the latter case, a warning is used if (typically graphical) arguments are specified that only apply to the plot = TRUE case. labels logical or character string. 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. warn.unused logical. If plot = FALSE and warn.unused = TRUE, a warning will be issued when graphical parameters are passed to hist.default(). ... further arguments and graphical parameters passed to plot.histogram and thence to title and axis (if plot = TRUE).

### 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 means ‘include highest’.

A numerical tolerance of 1e-7 times the median bin size (for more than four bins, otherwise the median is substituted) is applied when counting entries on the edges of bins. This is not included in the reported breaks nor in the calculation of density.

The default for breaks is "Sturges": see nclass.Sturges. Other names for which algorithms are supplied are "Scott" and "FD" / "Freedman-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 or the actual breakpoints 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). These are the nominal breaks, not with the boundary fuzz. counts n integers; for each cell, the number of x[] inside. density values 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; f^(x[i]) (b[i+1]-b[i])] = 1, where b[i] = breaks[i]. 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.

### 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), breaks = 12, col = "lightblue", border = "pink")
##-- For non-equidistant breaks, counts should NOT be graphed unscaled:
r <- hist(sqrt(islands), breaks = 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)

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

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

require(stats)
set.seed(14)
x <- rchisq(100, df = 4)

## Comparing data with a model distribution should be done with qqplot()!
qqplot(x, qchisq(ppoints(x), df = 4)); abline(0, 1, col = 2, lty = 2)

## if you really insist on using hist() ... :
hist(x, freq = FALSE, ylim = c(0, 0.2))
curve(dchisq(x, df = 4), col = 2, lty = 2, lwd = 2, add = TRUE)

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