Module peroxide::statistics::stat

Basic statistics

Statistics trait

• To make generic code, there is Statistics trait
  • mean: just mean
  • var : variance
  • sd : standard deviation (R-like notation)
  • cov : covariance
  • cor : correlation coefficient

  pub trait Statistics {
      type Array;
      type Value;
  
      fn mean(&self) -> Self::Value;
      fn var(&self) -> Self::Value;
      fn sd(&self) -> Self::Value;
      fn cov(&self) -> Self::Array;
      fn cor(&self) -> Self::Array;
  }

For Vec<f64>

• Caution: For Vec<f64>, cov & cor are unimplemented (those for Matrix)

  extern crate peroxide;
  use peroxide::*;
  
  fn main() {
      let a = c!(1,2,3,4,5);
      a.mean().print(); // 3
      a.var().print();  // 2.5
      a.sd().print();   // 1.5811388300841898
  }

• But there are other functions to calculate cov & cor

  extern crate peroxide;
  use peroxide::*;
  
  fn main() {
      let v1 = c!(1,2,3);
      let v2 = c!(3,2,1);
  
      cov(&v1, &v2).print(); // -0.9999999999999998
      cor(&v1, &v2).print(); // -0.9999999999999993
  }

For Matrix

• For Matrix, mean, var, sd means column operations

• cov means covariance matrix & cor means also correlation coefficient matrix

  extern crate peroxide;
  use peroxide::*;
  
  fn main() {
      let m = matrix(c!(1,2,3,3,2,1), 3, 2, Col);
  
      m.mean().print(); // [2, 2]
      m.var().print();  // [1.0000, 1.0000]
      m.sd().print();   // [1.0000, 1.0000]
  
      m.cov().print();
      //         c[0]    c[1]
      // r[0]  1.0000 -1.0000
      // r[1] -1.0000  1.0000
  
      m.cor().print();
      //         c[0]    c[1]
      // r[0]       1 -1.0000
      // r[1] -1.0000       1
  }

Traits

Statistics

Statistics Trait

Functions

cor	Pearson's correlation coefficient
cov	Covariance (to Value)
lm	R like linear regression