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The empirical CDF with tail correction, ensuring that its output is never 0 or 1.
EmpCDF(x)
A function with signature function(x) that returns \(F_n(x)\).
function(x)
numeric vector of observations
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) cdf(50)
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