pit: Probability integral transform

In smoothemplik: Smoothed Empirical Likelihood

Probability integral transform

Description

Probability integral transform

Usage

pit(x, xout = NULL)

Arguments

x	A numeric vector of data points.
xout	A numeric vector. If supplied, then the transformed function at the grid points different from x takes values equidistant between themselves and the ends of the interval to which they belong.

Value

A numeric vector of values strictly between 0 and 1 of the same length as xout (or x, if xout is NULL).

Examples

set.seed(2)
x1 <- c(4, 3, 7, 10, 2, 2, 7, 2, 5, 6)
x2 <- sample(c(0, 0.5, 1, 2, 2.5, 3, 3.5, 10, 100), 25, replace = TRUE)
l <- length(x1)
pit(x1)

plot(pit(x1), ecdf(x1)(x1), xlim = c(0, 1), ylim = c(0, 1), asp = 1)
abline(v = seq(0.5 / l, 1 - 0.5 / l, length.out = l), col = "#00000044", lty = 2)
abline(v = c(0, 1))
points(pit(x1, x2), ecdf(x1)(x2), pch = 16, col = "#CC000088", cex = 0.9)
abline(v = pit(x1, x2), col = "#CC000044", lty = 2)

x1 <- c(1, 1, 3, 4, 6)
x2 <- c(0, 2, 2, 5.9, 7, 8)
pit(x1)
pit(x1, x2)

set.seed(1)
l <- 10
x1 <- rlnorm(l)
x2 <- sample(c(x1, rlnorm(10)))
plot(pit(x1), ecdf(x1)(x1), xlim = c(0, 1), ylim = c(0, 1), asp = 1)
abline(v = seq(0.5 / l, 1 - 0.5 / l, length.out = l), col = "#00000044", lty = 2)
abline(v = c(0, 1))
points(pit(x1, x2), ecdf(x1)(x2), pch = 16, col = "#CC000088", cex = 0.9)

smoothemplik documentation built on Aug. 22, 2025, 1:11 a.m.