Corrected Empirical CDF — emp_cdf • rvinecopulib
Description: The empirical CDF with tail correction, ensuring that its output is never 0 or 1.

# Corrected Empirical CDF

Source: `R/tools.R`
`emp_cdf.Rd`

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

    emp_cdf(x)

## Arguments

x

  numeric vector of observations

## Value

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

## Details

The corrected empirical CDF is defined as $$ F_n(x) = \frac{1}{n + 1} \min\biggl\{1, \sum_{i = 1}^n 1(X_i \le x)\biggr\} $$

## Examples

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

    # output is bounded away from 0 and 1
    cdf(-50)
    #> [1] 0.00990099
    cdf(50)
    #> [1] 0.990099