EmpCDF: Corrected Empirical CDF

In VineCopula: Statistical Inference of Vine Copulas

Corrected Empirical CDF

Description

The empirical CDF with tail correction, ensuring that its output is never 0 or 1.

Usage

EmpCDF(x)

Arguments

x	numeric vector of observations

Details

The corrected empirical CDF is defined as

F_n(x) = \frac{1}{n + 1} \min\biggl\{1, \sum_{i = 1}^n 1(X_i \le x)\biggr\}

Value

A function with signature ⁠function(x)⁠ that returns F_n(x).

Examples

# fit ECDF on simulated data
x <- rnorm(100)
cdf <- EmpCDF(x)

# output is bounded away from 0 and 1
cdf(-50)
cdf(50)

VineCopula documentation built on Sept. 11, 2024, 5:26 p.m.