1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302
#![allow(missing_docs)]
use std::mem;
#[cfg(test)]
mod tests;
fn local_sort(v: &mut [f64]) {
v.sort_by(|x: &f64, y: &f64| x.total_cmp(y));
}
/// Trait that provides simple descriptive statistics on a univariate set of numeric samples.
pub trait Stats {
/// Sum of the samples.
///
/// Note: this method sacrifices performance at the altar of accuracy
/// Depends on IEEE 754 arithmetic guarantees. See proof of correctness at:
/// ["Adaptive Precision Floating-Point Arithmetic and Fast Robust Geometric
/// Predicates"][paper]
///
/// [paper]: https://www.cs.cmu.edu/~quake-papers/robust-arithmetic.ps
fn sum(&self) -> f64;
/// Minimum value of the samples.
fn min(&self) -> f64;
/// Maximum value of the samples.
fn max(&self) -> f64;
/// Arithmetic mean (average) of the samples: sum divided by sample-count.
///
/// See: <https://en.wikipedia.org/wiki/Arithmetic_mean>
fn mean(&self) -> f64;
/// Median of the samples: value separating the lower half of the samples from the higher half.
/// Equal to `self.percentile(50.0)`.
///
/// See: <https://en.wikipedia.org/wiki/Median>
fn median(&self) -> f64;
/// Variance of the samples: bias-corrected mean of the squares of the differences of each
/// sample from the sample mean. Note that this calculates the _sample variance_ rather than the
/// population variance, which is assumed to be unknown. It therefore corrects the `(n-1)/n`
/// bias that would appear if we calculated a population variance, by dividing by `(n-1)` rather
/// than `n`.
///
/// See: <https://en.wikipedia.org/wiki/Variance>
fn var(&self) -> f64;
/// Standard deviation: the square root of the sample variance.
///
/// Note: this is not a robust statistic for non-normal distributions. Prefer the
/// `median_abs_dev` for unknown distributions.
///
/// See: <https://en.wikipedia.org/wiki/Standard_deviation>
fn std_dev(&self) -> f64;
/// Standard deviation as a percent of the mean value. See `std_dev` and `mean`.
///
/// Note: this is not a robust statistic for non-normal distributions. Prefer the
/// `median_abs_dev_pct` for unknown distributions.
fn std_dev_pct(&self) -> f64;
/// Scaled median of the absolute deviations of each sample from the sample median. This is a
/// robust (distribution-agnostic) estimator of sample variability. Use this in preference to
/// `std_dev` if you cannot assume your sample is normally distributed. Note that this is scaled
/// by the constant `1.4826` to allow its use as a consistent estimator for the standard
/// deviation.
///
/// See: <https://en.wikipedia.org/wiki/Median_absolute_deviation>
fn median_abs_dev(&self) -> f64;
/// Median absolute deviation as a percent of the median. See `median_abs_dev` and `median`.
fn median_abs_dev_pct(&self) -> f64;
/// Percentile: the value below which `pct` percent of the values in `self` fall. For example,
/// percentile(95.0) will return the value `v` such that 95% of the samples `s` in `self`
/// satisfy `s <= v`.
///
/// Calculated by linear interpolation between closest ranks.
///
/// See: <https://en.wikipedia.org/wiki/Percentile>
fn percentile(&self, pct: f64) -> f64;
/// Quartiles of the sample: three values that divide the sample into four equal groups, each
/// with 1/4 of the data. The middle value is the median. See `median` and `percentile`. This
/// function may calculate the 3 quartiles more efficiently than 3 calls to `percentile`, but
/// is otherwise equivalent.
///
/// See also: <https://en.wikipedia.org/wiki/Quartile>
fn quartiles(&self) -> (f64, f64, f64);
/// Inter-quartile range: the difference between the 25th percentile (1st quartile) and the 75th
/// percentile (3rd quartile). See `quartiles`.
///
/// See also: <https://en.wikipedia.org/wiki/Interquartile_range>
fn iqr(&self) -> f64;
}
/// Extracted collection of all the summary statistics of a sample set.
#[derive(Debug, Clone, PartialEq, Copy)]
#[allow(missing_docs)]
pub struct Summary {
pub sum: f64,
pub min: f64,
pub max: f64,
pub mean: f64,
pub median: f64,
pub var: f64,
pub std_dev: f64,
pub std_dev_pct: f64,
pub median_abs_dev: f64,
pub median_abs_dev_pct: f64,
pub quartiles: (f64, f64, f64),
pub iqr: f64,
}
impl Summary {
/// Constructs a new summary of a sample set.
pub fn new(samples: &[f64]) -> Summary {
Summary {
sum: samples.sum(),
min: samples.min(),
max: samples.max(),
mean: samples.mean(),
median: samples.median(),
var: samples.var(),
std_dev: samples.std_dev(),
std_dev_pct: samples.std_dev_pct(),
median_abs_dev: samples.median_abs_dev(),
median_abs_dev_pct: samples.median_abs_dev_pct(),
quartiles: samples.quartiles(),
iqr: samples.iqr(),
}
}
}
impl Stats for [f64] {
// FIXME #11059 handle NaN, inf and overflow
fn sum(&self) -> f64 {
let mut partials = vec![];
for &x in self {
let mut x = x;
let mut j = 0;
// This inner loop applies `hi`/`lo` summation to each
// partial so that the list of partial sums remains exact.
for i in 0..partials.len() {
let mut y: f64 = partials[i];
if x.abs() < y.abs() {
mem::swap(&mut x, &mut y);
}
// Rounded `x+y` is stored in `hi` with round-off stored in
// `lo`. Together `hi+lo` are exactly equal to `x+y`.
let hi = x + y;
let lo = y - (hi - x);
if lo != 0.0 {
partials[j] = lo;
j += 1;
}
x = hi;
}
if j >= partials.len() {
partials.push(x);
} else {
partials[j] = x;
partials.truncate(j + 1);
}
}
let zero: f64 = 0.0;
partials.iter().fold(zero, |p, q| p + *q)
}
fn min(&self) -> f64 {
assert!(!self.is_empty());
self.iter().fold(self[0], |p, q| p.min(*q))
}
fn max(&self) -> f64 {
assert!(!self.is_empty());
self.iter().fold(self[0], |p, q| p.max(*q))
}
fn mean(&self) -> f64 {
assert!(!self.is_empty());
self.sum() / (self.len() as f64)
}
fn median(&self) -> f64 {
self.percentile(50_f64)
}
fn var(&self) -> f64 {
if self.len() < 2 {
0.0
} else {
let mean = self.mean();
let mut v: f64 = 0.0;
for s in self {
let x = *s - mean;
v += x * x;
}
// N.B., this is _supposed to be_ len-1, not len. If you
// change it back to len, you will be calculating a
// population variance, not a sample variance.
let denom = (self.len() - 1) as f64;
v / denom
}
}
fn std_dev(&self) -> f64 {
self.var().sqrt()
}
fn std_dev_pct(&self) -> f64 {
let hundred = 100_f64;
(self.std_dev() / self.mean()) * hundred
}
fn median_abs_dev(&self) -> f64 {
let med = self.median();
let abs_devs: Vec<f64> = self.iter().map(|&v| (med - v).abs()).collect();
// This constant is derived by smarter statistics brains than me, but it is
// consistent with how R and other packages treat the MAD.
let number = 1.4826;
abs_devs.median() * number
}
fn median_abs_dev_pct(&self) -> f64 {
let hundred = 100_f64;
(self.median_abs_dev() / self.median()) * hundred
}
fn percentile(&self, pct: f64) -> f64 {
let mut tmp = self.to_vec();
local_sort(&mut tmp);
percentile_of_sorted(&tmp, pct)
}
fn quartiles(&self) -> (f64, f64, f64) {
let mut tmp = self.to_vec();
local_sort(&mut tmp);
let first = 25_f64;
let a = percentile_of_sorted(&tmp, first);
let second = 50_f64;
let b = percentile_of_sorted(&tmp, second);
let third = 75_f64;
let c = percentile_of_sorted(&tmp, third);
(a, b, c)
}
fn iqr(&self) -> f64 {
let (a, _, c) = self.quartiles();
c - a
}
}
// Helper function: extract a value representing the `pct` percentile of a sorted sample-set, using
// linear interpolation. If samples are not sorted, return nonsensical value.
fn percentile_of_sorted(sorted_samples: &[f64], pct: f64) -> f64 {
assert!(!sorted_samples.is_empty());
if sorted_samples.len() == 1 {
return sorted_samples[0];
}
let zero: f64 = 0.0;
assert!(zero <= pct);
let hundred = 100_f64;
assert!(pct <= hundred);
if pct == hundred {
return sorted_samples[sorted_samples.len() - 1];
}
let length = (sorted_samples.len() - 1) as f64;
let rank = (pct / hundred) * length;
let lrank = rank.floor();
let d = rank - lrank;
let n = lrank as usize;
let lo = sorted_samples[n];
let hi = sorted_samples[n + 1];
lo + (hi - lo) * d
}
/// Winsorize a set of samples, replacing values above the `100-pct` percentile
/// and below the `pct` percentile with those percentiles themselves. This is a
/// way of minimizing the effect of outliers, at the cost of biasing the sample.
/// It differs from trimming in that it does not change the number of samples,
/// just changes the values of those that are outliers.
///
/// See: <https://en.wikipedia.org/wiki/Winsorising>
pub fn winsorize(samples: &mut [f64], pct: f64) {
let mut tmp = samples.to_vec();
local_sort(&mut tmp);
let lo = percentile_of_sorted(&tmp, pct);
let hundred = 100_f64;
let hi = percentile_of_sorted(&tmp, hundred - pct);
for samp in samples {
if *samp > hi {
*samp = hi
} else if *samp < lo {
*samp = lo
}
}
}