pp_qq_plot function

P-P and Q-Q Plots

Probability-probability plots and quantile-quantile plots.

pp_plot(x, FUN, pch = 20, xlab = "Theoretical probabilities",
        ylab = "Sample probabilities", ...)
qq_plot(x, FUN = qnorm, method = c("theoretical", "empirical"),
        pch = 20, do.qqline = TRUE, qqline.args = NULL,
        xlab = "Theoretical quantiles", ylab = "Sample quantiles",
        ...)

Arguments

• x: data vector.

• FUN: function. For

  • pp_plot():: The distribution function (vectorized).
  • qq_plot():: The quantile function (vectorized).

• pch: plot symbol.

• xlab: x-axis label.

• ylab: y-axis label.

• do.qqline: logical indicating whether a Q-Q line is plotted.

• method: method used to construct the Q-Q line. If "theoretical", the theoretically true line with intercept 0 and slope 1 is displayed; if "empirical", the intercept and slope are determined with qqline(). The former helps deciding whether x comes from the distribution specified by FUN exactly, the latter whether x

  comes from a location-scale transformed distribution specified by FUN.

• qqline.args: list containing additional arguments passed to the underlying abline() functions. Defaults to list(a = 0, b = 1) if method = "theoretical" and list()

  if method = "empirical".

• ...: additional arguments passed to the underlying plot().

Returns

invisible().

Details

Note that Q-Q plots are more widely used than P-P plots (as they highlight deviations in the tails more clearly).

Author(s)

Marius Hofert

Examples

## Generate data
n <- 1000
mu <- 1
sig <- 3
nu <- 3.5
set.seed(271) # set seed
x <- mu + sig * sqrt((nu-2)/nu) * rt(n, df = nu) # sample from t_nu(mu, sig^2)

## P-P plot
pF <- function(q) pt((q - mu) / (sig * sqrt((nu-2)/nu)), df = nu)
pp_plot(x, FUN = pF)

## Q-Q plot
qF <- function(p) mu + sig * sqrt((nu-2)/nu) * qt(p, df = nu)
qq_plot(x, FUN = qF)

## A comparison with R's qqplot() and qqline()
qqplot(qF(ppoints(length(x))), x) # the same (except labels)
qqline(x, distribution = qF) # slightly different (since *estimated*)

## Difference of the two methods
set.seed(271)
z <- rnorm(1000)
## Standardized data
qq_plot(z, FUN = qnorm) # fine
qq_plot(z, FUN = qnorm, method = "empirical") # fine
## Location-scale transformed data
mu <- 3
sig <- 2
z. <- mu+sig*z
qq_plot(z., FUN = qnorm) # not fine (z. comes from N(mu, sig^2), not N(0,1))
qq_plot(z., FUN = qnorm, method = "empirical") # fine (as intercept and slope are estimated)