63 lines
2.7 KiB
Rust
63 lines
2.7 KiB
Rust
use crate::probability::binomial;
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use std::cmp::min;
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/// choose exactly w items (of a max of m) given k trials and n total items for a process that can be characterized by the `hypergeometric distribution`:
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/// That is:
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/// * The result of each draw (the elements of the population being sampled) can be classified into one of two mutually exclusive categories (e.g. Red/Blue or Not Red/Red).
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/// * The probability of a success changes on each draw, as each draw decreases the population (sampling without replacement from a finite population).
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pub fn exactly_without_replacement(x: u64, m: u64, k: u64, n: u64) -> rug::Float {
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// println!("Selecting exactly {} (out of {}) from {} samples of {}",x,m,k,n);
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if x > k || k > n || m > n || m < x {
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return rug::Float::with_val(64, 0.0);
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}
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// If the desired population is the same as the total population then the answer is trivial
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if m == n {
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return rug::Float::with_val(64, 1.0);
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}
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let mchoosen = binomial::nchoosek(m, x) * rug::Float::with_val(64, 1.0);
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let nsubmchooseksubx = binomial::nchoosek(n - m, k - x) * rug::Float::with_val(64, 1.0);
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let nchoosek = binomial::nchoosek(n, k) * rug::Float::with_val(64, 1.0);
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(mchoosen * nsubmchooseksubx) / nchoosek
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}
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/// choose at least w items (of a max of m) given k trials and n total items for a process that can be characterized by the `hypergeometric distribution`:
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/// That is:
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/// * The result of each draw (the elements of the population being sampled) can be classified into one of two mutually exclusive categories (e.g. Red/Blue or Not Red/Red).
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/// * The probability of a success changes on each draw, as each draw decreases the population (sampling without replacement from a finite population).
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/// This implementation is based on summing over `exactly_without_replacement`.
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pub fn at_least_without_replacement(w: u64, m: u64, k: u64, n: u64) -> rug::Float {
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// println!("Selecting at least {} (out of {}) from {} samples of {}",w,m,k,n);
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let mut prob_at_least = rug::Float::with_val(64, 0.0);
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if m == k && k == n || m == n {
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return rug::Float::with_val(64, 1.0);
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}
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if w == m {
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return exactly_without_replacement(w, m, k, n);
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}
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for x in w..=min(m, k) {
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let a = exactly_without_replacement(x, m, k, n);
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prob_at_least += a;
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}
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prob_at_least
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}
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#[cfg(test)]
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mod tests {
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use crate::probability::hypergeometric::at_least_without_replacement;
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#[test]
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fn test_at_least_without_replacement() {
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println!("{:.12}", at_least_without_replacement(2, 3, 3, 4).to_f64());
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}
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#[test]
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fn test_at_least_without_replacement_2() {
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println!("{:.12}", at_least_without_replacement(1, 1, 3, 9).to_f64());
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}
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}
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