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Plot an Empirical Quantile Function

Source: R/geom_ecdf.R
geom_eqf.Rd

geom_eqf() computes the empirical quantile function of a sample and renders it as a left-continuous step function on \([0, 1]\), using the same visual conventions as geom_qf_discrete(): horizontal segments, dashed vertical jumps, closed circles at the bottom of each jump (value achieved), and open circles at the top (next value not yet reached). An optional simultaneous confidence band is drawn using the Kolmogorov-Smirnov construction.

Usage

geom_eqf(
  mapping = NULL,
  data = NULL,
  stat = StatEQF,
  position = "identity",
  ...,
  na.rm = FALSE,
  show.legend = NA,
  inherit.aes = TRUE,
  open_fill = NULL,
  vert_type = "dashed",
  show_points = NULL,
  show_vert = NULL,
  conf_int = TRUE,
  level = 0.95,
  conf_alpha = 0.4
)

StatEQF

StatEQFBand

Format

An object of class StatEQF (inherits from Stat, ggproto, gg) of length 3.

An object of class StatEQFBand (inherits from Stat, ggproto, gg) of length 3.

Arguments

mapping

Set of aesthetic mappings created by aes(). If specified and inherit.aes = TRUE (the default), it is combined with the default mapping at the top level of the plot. You must supply mapping if there is no plot mapping.

data

The data to be displayed in this layer. There are three options:

  • NULL (default): the data is inherited from the plot data as specified in the call to ggplot().

  • A data.frame, or other object, will override the plot data. All objects will be fortified to produce a data frame. See fortify() for which variables will be created.

  • A function will be called with a single argument, the plot data. The return value must be a data.frame, and will be used as the layer data. A function can be created from a formula (e.g. ~ head(.x, 10)).

stat

The statistical transformation to use on the data for this layer. When using a geom_*() function to construct a layer, the stat argument can be used to override the default coupling between geoms and stats. The stat argument accepts the following:

  • A Stat ggproto subclass, for example StatCount.

  • A string naming the stat. To give the stat as a string, strip the function name of the stat_ prefix. For example, to use stat_count(), give the stat as "count".

  • For more information and other ways to specify the stat, see the layer stat documentation.

position

A position adjustment to use on the data for this layer. This can be used in various ways, including to prevent overplotting and improving the display. The position argument accepts the following:

  • The result of calling a position function, such as position_jitter(). This method allows for passing extra arguments to the position.

  • A string naming the position adjustment. To give the position as a string, strip the function name of the position_ prefix. For example, to use position_jitter(), give the position as "jitter".

  • For more information and other ways to specify the position, see the layer position documentation.

...

Other arguments passed on to layer()'s params argument. These arguments broadly fall into one of 4 categories below. Notably, further arguments to the position argument, or aesthetics that are required can not be passed through .... Unknown arguments that are not part of the 4 categories below are ignored.

  • Static aesthetics that are not mapped to a scale, but are at a fixed value and apply to the layer as a whole. For example, colour = "red" or linewidth = 3. The geom's documentation has an Aesthetics section that lists the available options. The 'required' aesthetics cannot be passed on to the params. Please note that while passing unmapped aesthetics as vectors is technically possible, the order and required length is not guaranteed to be parallel to the input data.

  • When constructing a layer using a stat_*() function, the ... argument can be used to pass on parameters to the geom part of the layer. An example of this is stat_density(geom = "area", outline.type = "both"). The geom's documentation lists which parameters it can accept.

  • Inversely, when constructing a layer using a geom_*() function, the ... argument can be used to pass on parameters to the stat part of the layer. An example of this is geom_area(stat = "density", adjust = 0.5). The stat's documentation lists which parameters it can accept.

  • The key_glyph argument of layer() may also be passed on through .... This can be one of the functions described as key glyphs, to change the display of the layer in the legend.

na.rm

If TRUE, silently remove missing values. Defaults to FALSE.

show.legend

Logical. Should this layer be included in the legends? NA, the default, includes if any aesthetics are mapped. FALSE never includes, and TRUE always includes. It can also be a named logical vector to finely select the aesthetics to display. To include legend keys for all levels, even when no data exists, use TRUE. If NA, all levels are shown in legend, but unobserved levels are omitted.

inherit.aes

If FALSE, overrides the default aesthetics, rather than combining with them. This is most useful for helper functions that define both data and aesthetics and shouldn't inherit behaviour from the default plot specification, e.g. annotation_borders().

open_fill

Fill color for the open (hollow) endpoint circles. Defaults to NULL, which uses the active theme's panel background color.

vert_type

Line type for the vertical jump segments. Defaults to "dashed".

show_points

Logical. If FALSE, suppresses all endpoint circles. If NULL (the default), circles are shown when there are 50 or fewer points and hidden otherwise.

show_vert

Logical. If FALSE, suppresses the vertical jump segments. If NULL (the default), segments are shown when there are 50 or fewer points and hidden otherwise.

conf_int

Logical. If TRUE (the default), draws a simultaneous KS confidence band around the ECDF.

level

Confidence level for the band. Defaults to 0.95.

conf_alpha

Alpha (transparency) of the confidence ribbon. Defaults to 0.4.

Value

A ggplot2 layer, or a list of two layers when conf_int = TRUE.

Details

The empirical quantile function is the left-continuous inverse of the empirical CDF: \(Q(p) = \inf\{x : F_n(x) \geq p\}\).

The confidence band at probability level \(p\) is \([Q_n(p - \varepsilon),\, Q_n(p + \varepsilon)]\), where \(\varepsilon = \sqrt{\log(2/\alpha) / (2n)}\) is the KS half-width (\(\alpha = 1 - \texttt{level}\)). This follows directly from inverting the simultaneous ECDF confidence band.

Examples

set.seed(1)
df <- data.frame(x = rnorm(50))

ggplot(df, aes(x = x)) + geom_eqf()


# Compare two groups
df2 <- data.frame(
  x     = c(rnorm(40), rnorm(40, mean = 2)),
  group = rep(c("A", "B"), each = 40)
)
ggplot(df2, aes(x = x, colour = group)) + geom_eqf()