The empirical CDF with tail correction, ensuring that its output is never 0 or 1.
EmpCDF(x)numeric vector of observations
A function with signature function(x) that returns \(F_n(x)\).
The corrected empirical CDF is defined as $$ F_n(x) = \frac{1}{n + 1} \min\biggl\{1, \sum_{i = 1}^n 1(X_i \le x)\biggr\} $$
# fit ECDF on simulated data
x <- rnorm(100)
cdf <- EmpCDF(x)
# output is bounded away from 0 and 1
cdf(-50)
#> [1] 0.00990099
cdf(50)
#> [1] 0.990099