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hist: Histograms

hist	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 = "lightgray", 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; as the breakpoints will be set to `pretty` values, the number is limited to `1e6` (with a warning if it was larger). If `breaks` is a function, the `x` vector is supplied to it as the only argument (and the number of breaks is only limited by the amount of available memory).
`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`	main title and axis labels: these arguments to `title()` get “smart” defaults here, e.g., the default `ylab` is `"Frequency"` iff `freq` is true.
`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

## Extreme outliers; the "FD" rule would take very large number of 'breaks':
XXL <- c(1:9, c(-1,1)*1e300)
hh <- hist(XXL, "FD") # did not work in R <= 3.4.1; now gives warning
## pretty() determines how many counts are used (platform dependently!):
length(hh$breaks) ## typically 1 million -- though 1e6 was "a suggestion only"

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)