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François Mockers 2020-05-14 22:13:20 +02:00
parent ae712f77a2
commit c757645587
1 changed files with 8 additions and 5 deletions
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13
world/src/sim/util.rs
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@ -25,7 +25,7 @@ pub fn map_edge_factor(posi: usize) -> 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
/// 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
@ -37,23 +37,26 @@ pub fn map_edge_factor(posi: usize) -> f32 {
///
/// NOTE:
///
/// Per [1], the problem of determing the CDF of
/// Per [[1]], the problem of determing 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],
/// 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/,
/// 1. [https://www.r-bloggers.com/sums-of-random-variables/][1],
/// 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. hhttps://en.wikipedia.org/wiki/Cumulative_distribution_function
/// 3. [https://en.wikipedia.org/wiki/Cumulative_distribution_function][3]
///
/// [1]: https://www.r-bloggers.com/sums-of-random-variables/
/// [3]: https://en.wikipedia.org/wiki/Cumulative_distribution_function
pub fn cdf_irwin_hall<const N: usize>(weights: &[f32; N], samples: [f32; N]) -> f32 {
// Let J_k = {(j_1, ... , j_k) : 1 ≤ j_1 < j_2 < ··· < j_k ≤ N }.
//