# hist

##### Histograms

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.

- Keywords
- hplot, distribution, dplot

##### Usage

`hist(x, …)`# S3 method for default
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; 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
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 \(10^{-7}\) 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:

the \(n+1\) cell boundaries (= `breaks`

if that
was a vector). These are the nominal breaks, not with the boundary fuzz.

\(n\) integers; for each cell, the number of
`x[]`

inside.

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]`

.

the \(n\) cell midpoints.

a character string with the actual `x`

argument name.

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.

##### See Also

`nclass.Sturges`

, `stem`

,
`density`

, `truehist`

in package
MASS.

Typical plots with vertical bars are *not* histograms. Consider
`barplot`

or `plot(*, type = "h")`

for such bar plots.

##### Examples

`library(graphics)`

```
# NOT RUN {
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$breaks)) # == 1
lines(r, lty = 3, border = "purple") # -> lines.histogram(*)
par(op)
require(utils) # for str
str(hist(islands, breaks = 12, plot = FALSE)) #-> 10 (~= 12) breaks
str(hist(islands, breaks = c(12,20,36,80,200,1000,17000), plot = FALSE))
hist(islands, breaks = c(12,20,36,80,200,1000,17000), freq = TRUE,
main = "WRONG histogram") # and warning
# }
# NOT RUN {
<!-- % save 2 seconds -->
## Extreme outliers; the "FD" rule would take very large number of 'breaks':
XXL <- c(1:9, c(-1,1)*1e300)
hh <- hist(XXL, "FD") # did not work in R <= 3.4.1; now gives warning
## pretty() determines how many counts are used (platform dependently!):
length(hh$breaks) ## typically 1 million -- though 1e6 was "a suggestion only"
# }
# NOT RUN {
require(stats)
set.seed(14)
x <- rchisq(100, df = 4)
# }
# NOT RUN {
## 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)
# }
```

*Documentation reproduced from package graphics, version 3.5.2, License: Part of R 3.5.2*