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#[derive(Debug, Clone)]
#[cfg_attr(feature = "serde1", derive(Serialize, Deserialize))]
pub struct Kurtosis {
avg: Skewness,
sum_4: f64,
}
impl Kurtosis {
#[inline]
pub fn new() -> Kurtosis {
Kurtosis {
avg: Skewness::new(),
sum_4: 0.,
}
}
#[inline]
fn increment(&mut self) {
self.avg.increment();
}
#[inline]
fn add_inner(&mut self, delta: f64, delta_n: f64) {
let n = self.len().to_f64().unwrap();
let term = delta * delta_n * (n - 1.);
let delta_n_sq = delta_n*delta_n;
self.sum_4 += term * delta_n_sq * (n*n - 3.*n + 3.)
+ 6. * delta_n_sq * self.avg.avg.sum_2
- 4. * delta_n * self.avg.sum_3;
self.avg.add_inner(delta, 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_mean()
}
#[inline]
pub fn skewness(&self) -> f64 {
self.avg.skewness()
}
#[inline]
pub fn kurtosis(&self) -> f64 {
if self.sum_4 == 0. {
return 0.;
}
let n = self.len().to_f64().unwrap();
n * self.sum_4 / (self.avg.avg.sum_2 * self.avg.avg.sum_2) - 3.
}
}
impl core::default::Default for Kurtosis {
fn default() -> Kurtosis {
Kurtosis::new()
}
}
impl Estimate for Kurtosis {
#[inline]
fn add(&mut self, x: f64) {
let delta = x - self.mean();
self.increment();
let n = self.len().to_f64().unwrap();
self.add_inner(delta, delta/n);
}
#[inline]
fn estimate(&self) -> f64 {
self.kurtosis()
}
}
impl Merge for Kurtosis {
#[inline]
fn merge(&mut self, other: &Kurtosis) {
let len_self = self.len().to_f64().unwrap();
let len_other = other.len().to_f64().unwrap();
let len_total = len_self + len_other;
let delta = other.mean() - self.mean();
let delta_n = delta / len_total;
let delta_n_sq = delta_n * delta_n;
self.sum_4 += other.sum_4
+ delta * delta_n*delta_n_sq * len_self*len_other
* (len_self*len_self - len_self*len_other + len_other*len_other)
+ 6.*delta_n_sq * (len_self*len_self * other.avg.avg.sum_2 + len_other*len_other * self.avg.avg.sum_2)
+ 4.*delta_n * (len_self * other.avg.sum_3 - len_other * self.avg.sum_3);
self.avg.merge(&other.avg);
}
}
impl_from_iterator!(Kurtosis);
impl_from_par_iterator!(Kurtosis);