covarPopStable

Introduced in: v1.1

Calculates the population covariance:

\frac{\Sigma{(x - \bar{x})(y - \bar{y})}}{n}

It is similar to the covarPop function, but uses a numerically stable algorithm. As a result, covarPopStable is slower than covarPop but produces a more accurate result.

Syntax

covarPopStable(x, y)

Arguments

x — First variable. (U)Int* or Float* or Decimal
y — Second variable. (U)Int* or Float* or Decimal

Returned value

Returns the population covariance between x and y. Float64

Examples

Basic population covariance calculation with stable algorithm

DROP TABLE IF EXISTS series;
CREATE TABLE series(i UInt32, x_value Float64, y_value Float64) ENGINE = Memory;
INSERT INTO series(i, x_value, y_value) VALUES (1, 5.6,-4.4),(2, -9.6,3),(3, -1.3,-4),(4, 5.3,9.7),(5, 4.4,0.037),(6, -8.6,-7.8),(7, 5.1,9.3),(8, 7.9,-3.6),(9, -8.2,0.62),(10, -3,7.3);

SELECT covarPopStable(x_value, y_value)
FROM series

┌─covarPopStable(x_value, y_value)─┐
│                         6.485648 │
└──────────────────────────────────┘

covarPopStable​

covarPopStable