7 Statistics

7.1 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;
}

7.1.1 For Vec<f64>

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

    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

    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
}

    • 7.1.2 For Matrix

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

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

      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
}