calculate_tv_distance_empirical: Calculate Total Variation (TV) Distance Empirically

In covalchemy: Constructing Joint Distributions with Control Over Statistical Properties

Calculate Total Variation (TV) Distance Empirically

Description

This function calculates the Total Variation (TV) distance between the empirical cumulative distribution functions (ECDFs) of two datasets: original data and generated data. The TV distance is defined as half the sum of the absolute differences between the two CDFs at each point in the domain.

Usage

calculate_tv_distance_empirical(original_data, generated_data)

Arguments

original_data	A numeric vector of the original data.
generated_data	A numeric vector of the generated data.

Value

A numeric value representing the Total Variation distance between the empirical CDFs of the original and generated data.

Examples

# Test Case 1: Data from similar distributions
original_data <- rnorm(1000, mean = 0, sd = 1)  # Normal distribution (mean = 0, sd = 1)
generated_data <- rnorm(1000, mean = 0, sd = 1)  # Similar normal distribution
tv_distance <- calculate_tv_distance_empirical(original_data, generated_data)
print(tv_distance)  # Expected to be close to 0, as both datasets are similar

# Test Case 2: Data from different distributions
original_data <- rnorm(1000, mean = 0, sd = 1)  # Normal distribution (mean = 0, sd = 1)
generated_data <- rnorm(1000, mean = 5, sd = 2)  # Different normal distribution
tv_distance <- calculate_tv_distance_empirical(original_data, generated_data)
print(tv_distance)  # Expected to be larger, as the datasets are quite different

covalchemy documentation built on April 12, 2025, 2:15 a.m.