pp_qq_plot: P-P and Q-Q Plots

In qrmtools: Tools for Quantitative Risk Management

P-P and Q-Q Plots

Description

Probability-probability plots and quantile-quantile plots.

Usage

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().

Details

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

Value

invisible().

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)

qrmtools documentation built on May 29, 2024, 9:35 a.m.