covarSampStable

Calculates the value of Σ((x - x̅)(y - y̅)) / (n - 1). Similar to covarSamp but works slower while providing a lower computational error.

Syntax

covarSampStable(x, y)

Arguments

x — first variable. (U)Int*, Float*, Decimal.
y — second variable. (U)Int*, Float*, Decimal.

Returned Value

The sample covariance between x and y. For n <= 1, inf is returned. Float64.

Example

Query:

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 covarSampStable(x_value, y_value)
FROM
(
    SELECT
        x_value,
        y_value
    FROM series
);

Result:

┌─covarSampStable(x_value, y_value)─┐
│                 7.206275555555556 │
└───────────────────────────────────┘

Query:

SELECT covarSampStable(x_value, y_value)
FROM
(
    SELECT
        x_value,
        y_value
    FROM series LIMIT 1
);

Result:

┌─covarSampStable(x_value, y_value)─┐
│                               inf │
└───────────────────────────────────┘

covarSampStable

Introduced in: v1.1

Calculates the sample covariance:

\frac{\Sigma{(x - \bar{x})(y - \bar{y})}}{n - 1}

It is similar to covarSamp but uses a numerically stable algorithm. As a result, covarSampStable is slower than covarSamp but provides a lower computational error.

Syntax

covarSampStable(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 sample covariance between x and y. For n <= 1, inf is returned. Float64

Examples

Basic sample 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 covarSampStable(x_value, y_value)
FROM
(
    SELECT
        x_value,
        y_value
    FROM series
);

┌─covarSampStable(x_value, y_value)─┐
│                 7.206275555555556 │
└───────────────────────────────────┘

Single value returns inf

SELECT covarSampStable(x_value, y_value)
FROM
(
    SELECT
        x_value,
        y_value
    FROM series LIMIT 1
);

┌─covarSampStable(x_value, y_value)─┐
│                               inf │
└───────────────────────────────────┘

covarSampStable​

covarSampStable