1 #![allow(missing_docs)]
2 #![allow(deprecated)] // Float
4 use std
::cmp
::Ordering
::{self, Equal, Greater, Less}
;
10 fn local_cmp(x
: f64, y
: f64) -> Ordering
{
11 // arbitrarily decide that NaNs are larger than everything.
14 } else if x
.is_nan() {
25 fn local_sort(v
: &mut [f64]) {
26 v
.sort_by(|x
: &f64, y
: &f64| local_cmp(*x
, *y
));
29 /// Trait that provides simple descriptive statistics on a univariate set of numeric samples.
31 /// Sum of the samples.
33 /// Note: this method sacrifices performance at the altar of accuracy
34 /// Depends on IEEE-754 arithmetic guarantees. See proof of correctness at:
35 /// ["Adaptive Precision Floating-Point Arithmetic and Fast Robust Geometric
36 /// Predicates"][paper]
38 /// [paper]: http://www.cs.cmu.edu/~quake-papers/robust-arithmetic.ps
41 /// Minimum value of the samples.
44 /// Maximum value of the samples.
47 /// Arithmetic mean (average) of the samples: sum divided by sample-count.
49 /// See: <https://en.wikipedia.org/wiki/Arithmetic_mean>
50 fn mean(&self) -> f64;
52 /// Median of the samples: value separating the lower half of the samples from the higher half.
53 /// Equal to `self.percentile(50.0)`.
55 /// See: <https://en.wikipedia.org/wiki/Median>
56 fn median(&self) -> f64;
58 /// Variance of the samples: bias-corrected mean of the squares of the differences of each
59 /// sample from the sample mean. Note that this calculates the _sample variance_ rather than the
60 /// population variance, which is assumed to be unknown. It therefore corrects the `(n-1)/n`
61 /// bias that would appear if we calculated a population variance, by dividing by `(n-1)` rather
64 /// See: <https://en.wikipedia.org/wiki/Variance>
67 /// Standard deviation: the square root of the sample variance.
69 /// Note: this is not a robust statistic for non-normal distributions. Prefer the
70 /// `median_abs_dev` for unknown distributions.
72 /// See: <https://en.wikipedia.org/wiki/Standard_deviation>
73 fn std_dev(&self) -> f64;
75 /// Standard deviation as a percent of the mean value. See `std_dev` and `mean`.
77 /// Note: this is not a robust statistic for non-normal distributions. Prefer the
78 /// `median_abs_dev_pct` for unknown distributions.
79 fn std_dev_pct(&self) -> f64;
81 /// Scaled median of the absolute deviations of each sample from the sample median. This is a
82 /// robust (distribution-agnostic) estimator of sample variability. Use this in preference to
83 /// `std_dev` if you cannot assume your sample is normally distributed. Note that this is scaled
84 /// by the constant `1.4826` to allow its use as a consistent estimator for the standard
87 /// See: <http://en.wikipedia.org/wiki/Median_absolute_deviation>
88 fn median_abs_dev(&self) -> f64;
90 /// Median absolute deviation as a percent of the median. See `median_abs_dev` and `median`.
91 fn median_abs_dev_pct(&self) -> f64;
93 /// Percentile: the value below which `pct` percent of the values in `self` fall. For example,
94 /// percentile(95.0) will return the value `v` such that 95% of the samples `s` in `self`
97 /// Calculated by linear interpolation between closest ranks.
99 /// See: <http://en.wikipedia.org/wiki/Percentile>
100 fn percentile(&self, pct
: f64) -> f64;
102 /// Quartiles of the sample: three values that divide the sample into four equal groups, each
103 /// with 1/4 of the data. The middle value is the median. See `median` and `percentile`. This
104 /// function may calculate the 3 quartiles more efficiently than 3 calls to `percentile`, but
105 /// is otherwise equivalent.
107 /// See also: <https://en.wikipedia.org/wiki/Quartile>
108 fn quartiles(&self) -> (f64, f64, f64);
110 /// Inter-quartile range: the difference between the 25th percentile (1st quartile) and the 75th
111 /// percentile (3rd quartile). See `quartiles`.
113 /// See also: <https://en.wikipedia.org/wiki/Interquartile_range>
114 fn iqr(&self) -> f64;
117 /// Extracted collection of all the summary statistics of a sample set.
118 #[derive(Debug, Clone, PartialEq, Copy)]
119 #[allow(missing_docs)]
128 pub std_dev_pct
: f64,
129 pub median_abs_dev
: f64,
130 pub median_abs_dev_pct
: f64,
131 pub quartiles
: (f64, f64, f64),
136 /// Construct a new summary of a sample set.
137 pub fn new(samples
: &[f64]) -> Summary
{
142 mean
: samples
.mean(),
143 median
: samples
.median(),
145 std_dev
: samples
.std_dev(),
146 std_dev_pct
: samples
.std_dev_pct(),
147 median_abs_dev
: samples
.median_abs_dev(),
148 median_abs_dev_pct
: samples
.median_abs_dev_pct(),
149 quartiles
: samples
.quartiles(),
155 impl Stats
for [f64] {
156 // FIXME #11059 handle NaN, inf and overflow
157 fn sum(&self) -> f64 {
158 let mut partials
= vec
![];
163 // This inner loop applies `hi`/`lo` summation to each
164 // partial so that the list of partial sums remains exact.
165 for i
in 0..partials
.len() {
166 let mut y
: f64 = partials
[i
];
167 if x
.abs() < y
.abs() {
168 mem
::swap(&mut x
, &mut y
);
170 // Rounded `x+y` is stored in `hi` with round-off stored in
171 // `lo`. Together `hi+lo` are exactly equal to `x+y`.
173 let lo
= y
- (hi
- x
);
180 if j
>= partials
.len() {
184 partials
.truncate(j
+ 1);
188 partials
.iter().fold(zero
, |p
, q
| p
+ *q
)
191 fn min(&self) -> f64 {
192 assert
!(!self.is_empty());
193 self.iter().fold(self[0], |p
, q
| p
.min(*q
))
196 fn max(&self) -> f64 {
197 assert
!(!self.is_empty());
198 self.iter().fold(self[0], |p
, q
| p
.max(*q
))
201 fn mean(&self) -> f64 {
202 assert
!(!self.is_empty());
203 self.sum() / (self.len() as f64)
206 fn median(&self) -> f64 {
207 self.percentile(50_f64)
210 fn var(&self) -> f64 {
214 let mean
= self.mean();
215 let mut v
: f64 = 0.0;
220 // N.B., this is _supposed to be_ len-1, not len. If you
221 // change it back to len, you will be calculating a
222 // population variance, not a sample variance.
223 let denom
= (self.len() - 1) as f64;
228 fn std_dev(&self) -> f64 {
232 fn std_dev_pct(&self) -> f64 {
233 let hundred
= 100_f64;
234 (self.std_dev() / self.mean()) * hundred
237 fn median_abs_dev(&self) -> f64 {
238 let med
= self.median();
239 let abs_devs
: Vec
<f64> = self.iter().map(|&v
| (med
- v
).abs()).collect();
240 // This constant is derived by smarter statistics brains than me, but it is
241 // consistent with how R and other packages treat the MAD.
243 abs_devs
.median() * number
246 fn median_abs_dev_pct(&self) -> f64 {
247 let hundred
= 100_f64;
248 (self.median_abs_dev() / self.median()) * hundred
251 fn percentile(&self, pct
: f64) -> f64 {
252 let mut tmp
= self.to_vec();
253 local_sort(&mut tmp
);
254 percentile_of_sorted(&tmp
, pct
)
257 fn quartiles(&self) -> (f64, f64, f64) {
258 let mut tmp
= self.to_vec();
259 local_sort(&mut tmp
);
261 let a
= percentile_of_sorted(&tmp
, first
);
263 let b
= percentile_of_sorted(&tmp
, second
);
265 let c
= percentile_of_sorted(&tmp
, third
);
269 fn iqr(&self) -> f64 {
270 let (a
, _
, c
) = self.quartiles();
275 // Helper function: extract a value representing the `pct` percentile of a sorted sample-set, using
276 // linear interpolation. If samples are not sorted, return nonsensical value.
277 fn percentile_of_sorted(sorted_samples
: &[f64], pct
: f64) -> f64 {
278 assert
!(!sorted_samples
.is_empty());
279 if sorted_samples
.len() == 1 {
280 return sorted_samples
[0];
283 assert
!(zero
<= pct
);
284 let hundred
= 100_f64;
285 assert
!(pct
<= hundred
);
287 return sorted_samples
[sorted_samples
.len() - 1];
289 let length
= (sorted_samples
.len() - 1) as f64;
290 let rank
= (pct
/ hundred
) * length
;
291 let lrank
= rank
.floor();
292 let d
= rank
- lrank
;
293 let n
= lrank
as usize;
294 let lo
= sorted_samples
[n
];
295 let hi
= sorted_samples
[n
+ 1];
299 /// Winsorize a set of samples, replacing values above the `100-pct` percentile
300 /// and below the `pct` percentile with those percentiles themselves. This is a
301 /// way of minimizing the effect of outliers, at the cost of biasing the sample.
302 /// It differs from trimming in that it does not change the number of samples,
303 /// just changes the values of those that are outliers.
305 /// See: <http://en.wikipedia.org/wiki/Winsorising>
306 pub fn winsorize(samples
: &mut [f64], pct
: f64) {
307 let mut tmp
= samples
.to_vec();
308 local_sort(&mut tmp
);
309 let lo
= percentile_of_sorted(&tmp
, pct
);
310 let hundred
= 100_f64;
311 let hi
= percentile_of_sorted(&tmp
, hundred
- pct
);
312 for samp
in samples
{
315 } else if *samp
< lo
{