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#[derive(Debug, Clone)]
pub struct Skewness {
avg: MeanWithError,
sum_3: f64,
}
impl Skewness {
#[inline]
pub fn new() -> Skewness {
Skewness {
avg: MeanWithError::new(),
sum_3: 0.,
}
}
#[inline]
pub fn add(&mut self, x: f64) {
let delta = x - self.mean();
self.increment();
let n = f64::approx_from(self.len()).unwrap();
self.add_inner(delta, delta/n);
}
#[inline]
fn increment(&mut self) {
self.avg.increment();
}
#[inline]
fn add_inner(&mut self, delta: f64, delta_n: f64) {
let n = f64::approx_from(self.len()).unwrap();
let term = delta * delta_n * (n - 1.);
self.sum_3 += term * delta_n * (n - 2.)
- 3.*delta_n * self.avg.sum_2;
self.avg.add_inner(delta_n);
}
#[inline]
pub fn is_empty(&self) -> bool {
self.avg.is_empty()
}
#[inline]
pub fn mean(&self) -> f64 {
self.avg.mean()
}
#[inline]
pub fn len(&self) -> u64 {
self.avg.len()
}
#[inline]
pub fn sample_variance(&self) -> f64 {
self.avg.sample_variance()
}
#[inline]
pub fn population_variance(&self) -> f64 {
self.avg.population_variance()
}
#[inline]
pub fn error_mean(&self) -> f64 {
self.avg.error()
}
#[inline]
pub fn skewness(&self) -> f64 {
if self.sum_3 == 0. {
return 0.;
}
let n = f64::approx_from(self.len()).unwrap();
let sum_2 = self.avg.sum_2;
debug_assert!(sum_2 != 0.);
n.sqrt() * self.sum_3 / (sum_2*sum_2*sum_2).sqrt()
}
#[inline]
pub fn merge(&mut self, other: &Skewness) {
let len_self = f64::approx_from(self.len()).unwrap();
let len_other = f64::approx_from(other.len()).unwrap();
let len_total = len_self + len_other;
let delta = other.mean() - self.mean();
let delta_n = delta / len_total;
self.sum_3 += other.sum_3
+ delta*delta_n*delta_n * len_self*len_other*(len_self - len_other)
+ 3.*delta_n * (len_self * other.avg.sum_2 - len_other * self.avg.sum_2);
self.avg.merge(&other.avg);
}
}
impl core::iter::FromIterator<f64> for Skewness {
fn from_iter<T>(iter: T) -> Skewness
where T: IntoIterator<Item=f64>
{
let mut a = Skewness::new();
for i in iter {
a.add(i);
}
a
}
}