cov, scov

Covariance

cov

x cov y    cov[x;y]

Where x and y are conforming numeric lists returns their covariance as a floating-point number. Applies to all numeric data types and signals an error with temporal types, char and sym.

q)2 3 5 7 cov 3 3 5 9
4.5
q)2 3 5 7 cov 4 3 0 2
-1.8125
q)select price cov size by sym from trade

cov is an aggregate function.

The function cov is equivalent to {avg[x*y]-avg[x]*avg y}.

Domain and range:

    b g x h i j e f c s p m d z n u v t
----------------------------------------
b | f . f f f f f f f . f f f f f f f f
g | . . . . . . . . . . . . . . . . . .
x | f . f f f f f f f . f f f f f f f f
h | f . f f f f f f f . f f f f f f f f
i | f . f f f f f f f . f f f f f f f f
j | f . f f f f f f f . f f f f f f f f
e | f . f f f f f f f . f f f f f f f f
f | f . f f f f f f f . f f f f f f f f
c | f . f f f f f f f . f f f f f f f f
s | . . . . . . . . . . . . . . . . . .
p | f . f f f f f f f . f f f f f f f f
m | f . f f f f f f f . f f f f f f f f
d | f . f f f f f f f . f f f f f f f f
z | f . f f f f f f f . f f f f f f f f
n | f . f f f f f f f . f f f f f f f f
u | f . f f f f f f f . f f f f f f f f
v | f . f f f f f f f . f f f f f f f f
t | f . f f f f f f f . f f f f f f f f

Range: f

cov is a multithreaded primitive.

scov

Sample covariance

x scov y    scov[x;y]

Where x and y are conforming numeric lists returns their sample covariance as a float atom.

\[scov(x,y)=\frac{n}{n-1} cov(x,y)\]

Applies to all numeric data types and signals an error with temporal types, char and sym.

q)2 3 5 7 scov 3 3 5 9
6f
q)2 3 5 7 scov 4 3 0 2
-2.416667
q)select price scov size by sym from trade

scov is an aggregate function.

The function scov is equivalent to {cov[x;y]*count[x]%-1+count x}.

Domain and range:

    b g x h i j e f c s p m d z n u v t
----------------------------------------
b | f . f f f f f f . . f f f f f f f f
g | . . . . . . . . . . . . . . . . . .
x | f . f f f f f f . . f f f f f f f f
h | f . f f f f f f . . f f f f f f f f
i | f . f f f f f f . . f f f f f f f f
j | f . f f f f f f . . f f f f f f f f
e | f . f f f f f f . . f f f f f f f f
f | f . f f f f f f f . f f f f f f f f
c | . . . . . . . f . . f f f f f f f f
s | . . . . . . . . . . . . . . . . . .
p | f . f f f f f f f . f . . . f f f f
m | f . f f f f f f f . . f . . f f f f
d | f . f f f f f f f . . . f . f f f f
z | f . f f f f f f f . . . . f f f f f
n | f . f f f f f f f . f f f f f f f f
u | f . f f f f f f f . f f f f f f f f
v | f . f f f f f f f . f f f f f f f f
t | f . f f f f f f f . f f f f f f f f

Range: f

scov is a multithreaded primitive.

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var, svar
Mathematics
Covariance