Function veloren_world::sim::util::cdf_irwin_hall

pub fn cdf_irwin_hall<const N: usize>(
    weights: &[f32; N],
    samples: [f32; N]
) -> f32

Computes the cumulative distribution function of the weighted sum of k independent, uniformly distributed random variables between 0 and 1. For each variable i, we use weights[i] as the weight to give samples[i] (the weights should all be positive).

If the precondition is met, the distribution of the result of calling this function will be uniformly distributed while preserving the same information that was in the original average.

For N > 33 the function will no longer return correct results since we will overflow u32.

NOTE:

Per [1], the problem of determining the CDF of the sum of uniformly distributed random variables over different ranges is considerably more complicated than it is for the same-range case. Fortunately, it also provides a reference to [2], which contains a complete derivation of an exact rule for the density function for this case. The CDF is just the integral of the cumulative distribution function [3], which we use to convert this into a CDF formula.

This allows us to sum weighted, uniform, independent random variables.

At some point, we should probably contribute this back to stats-rs.

1. https://www.r-bloggers.com/sums-of-random-variables/,
2. Sadooghi-Alvandi, S., A. Nematollahi, & R. Habibi, 2009. On the Distribution of the Sum of Independent Uniform Random Variables. Statistical Papers, 50, 171-175.
3. https://en.wikipedia.org/wiki/Cumulative_distribution_function