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---------------------
Statistical Functions
---------------------
By the SQL specification, some statistical functions are defined.
Function about variance and standard deviation are bellow.
VAR_SAMP: return the sample variance.
eq. (SUM(<expr> ^ 2) - SUM(<expr>) ^ 2 / COUNT(<expr>)) / (COUNT(<expr>) - 1)
VAR_POP: return the population variance.
eq. (SUM(<expr> ^ 2) - SUM(<expr>) ^ 2 / COUNT(<expr>)) / COUNT(<expr>)
STDDEV_SAMP: return the sample standard deviation.
eq. SQRT(VAR_SAMP(<expr))
STDDEV_POP: return the population standard deviation.
eq. SQRT(VAR_POP(<expr>))
COVAR_SAMP: return the sample population.
eq. (SUM(<expr1> * <expr2>) - SUM(<expr1>) * SUM(<expr2>) / COUNT(*)) / (COUNT(*) - 1)
COVAR_POP: return the population covariance.
eq. (SUM(<expr1> * <expr2>) - SUM(<expr1>) * SUM(<expr2>) / COUNT(*)) / COUNT(*)
CORR: returns the coefficient of correlation.
eq. COVAR_POP(<expr1>, <expr2>) / (STDDEV_POP(<expr2>) * STDDEV_POP(<expr1>))
Author:
Hajime Nakagami <nakagami@gmail.com>
Syntax:
<single param statistical function> ::= <single param statistical function name>(<expr>)
<single param statistical function name> := { VAR_POP | VAR_SAMP | STDDEV_POP | STDDEV_SAMP }
<dual param statistical function> ::= <dual param statistical function name>(<expr1>, <expr2>)
<dual param statistical function name> := { COVAR_POP | COVAR_SAMP | CORR }
Note:
If VAR_SAMP, STDDEV_SAMP, COVAR_SAMP and result count is 0 or 1, return NULL.
If VAR_POP, STDDEV_POP, COVAR_POP, CORR and result count is 0, return NULL.
Example:
SELECT STDDEV_SAMP(salary) FROM employees;
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