R: Weighted Histograms

wtd.hist {weights} | R Documentation

## Weighted Histograms

### Description

Produces weighted histograms by adding a "weight" option to the his.default function from the graphics package (Copyright R-core). The code here was copied from that function and modified slightly to allow for weighted histograms as well as unweighted 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.

### Usage

    wtd.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, weight = 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`, 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. Additionally draw labels on top of bars, if not `FALSE`; see `plot.histogram` in the `graphics` package.
`nclass` | numeric (integer). For S(-PLUS) compatibility only, `nclass` is equivalent to `breaks` for a scalar or character argument.
`weight` | numeric. Defines a set of weights to produce a weighted histogram. Will default to 1 for each case if no other weight is defined.
`...` | 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 (weighted) counts in the cells defined by `breaks`. Thus the height of a rectangle is proportional to the (weighted) 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’.

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 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 values; for each cell, the number of `x[]` inside.
`density` | values for each bin such that the area under the histogram totals 1. \hat f(x_i ω_i) / f^(x[i] ω[i]), as estimated density values. If `all(diff(breaks) == 1)`, they are the relative frequencies `counts/n` and in general satisfy ∑_i \hat f(x_i ω_i) (b_{i+1}-b_i) = 1 / sum[i; f^(x[i] ω[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.

### Author(s)

Josh Pasek, Assistant Professor of Communication Studies at the University of Michigan (www.joshpasek.com) was responsible for the updates to the hist function necessary to implement weighted counts. The hist.default code from the graphics package on which the current function was based was written by R-core. All modifications are noted in code and the copyright for all original code remains with R-core.

### Examples

    var1 <- c(1:100)
    wgt <- var1/mean(var1)
    par(mfrow=c(2, 2))
    wtd.hist(var1)
    wtd.hist(var1, weight=wgt)
    wtd.hist(var1, weight=var1)

[Package weights version 1.0.2 Index]