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Empirical Cumulative Distribution Function (ECDF)

Source: R/empirical_cumulative_distribution_function.R
empirical_cumulative_distribution_function.Rd

Create an empirical cumulative distribution function (ECDF) from a given vector.

Usage

empirical_cumulative_distribution_function(data, sorted = FALSE)

Arguments

data

A numeric vector of data points.

sorted

A logical indicating whether the data is already sorted. Default is FALSE.

Value

An object representing the ECDF, with member function $ecdf(x) to evaluate the ECDF at point(s) x.

Details

The ECDF is a step function constructed from observed data that converges to the true CDF as sample size grows. It is commonly used in goodness-of-fit workflows that compare the empirical CDF to a hypothesised distribution.

Implementation Notes: Data must be sorted; by default the constructor sorts at $$O(n \log n)$$ cost. If the data is already sorted, set sorted = TRUE to avoid the sort. Evaluation uses binary search (upper_bound) and runs in $$O(\log n)$$ time.

Examples

data <- c(1.2, 2.3, 3.1, 4.5, 5.0)
ecdf_obj <- empirical_cumulative_distribution_function(data)
ecdf_obj$ecdf(3.0)  # Evaluate ECDF at x = 3.0
#> [1] 0.4