PostgreSQL aggregate function 2 : Aggregate Functions for Statistics

作者

digoal

日期

2015-03-03

背景

本文将讲解一下统计类的聚合函数.

在此前我分别以相关性函数corr和计算总体/样本方差, 标准方差的函数variance, var_pop, var_samp, stddev, stddev_pop, stddev_samp做过比较详细的讲解.

例如corr在数据库的物理存储顺序以及逻辑顺序的统计信息中就有应用. 请参考 :

http://blog.163.com/digoal@126/blog/static/163877040201512835135264/

http://blog.163.com/digoal@126/blog/static/163877040201512810112541/

PostgreSQL 9.4为例, 目前支持的统计学聚合函数表如下 :

这些函数的源码全部都在 src/backend/utils/adt/float.c .

这些统计学相关的术语, 算法可参考维基百科, 或百度百科.

Table 9-50. Aggregate Functions for Statistics

Function	Argument Type	Return Type	Description
corr(Y, X)	double precision	double precision	correlation coefficient
covar_pop(Y, X)	double precision	double precision	population covariance
covar_samp(Y, X)	double precision	double precision	sample covariance
regr_avgx(Y, X)	double precision	double precision	average of the independent variable (sum(X)/N)
regr_avgy(Y, X)	double precision	double precision	average of the dependent variable (sum(Y)/N)
regr_count(Y, X)	double precision	bigint	number of input rows in which both expressions are nonnull
regr_intercept(Y, X)	double precision	double precision	y-intercept of the least-squares-fit linear equation determined by the (X, Y) pairs
regr_r2(Y, X)	double precision	double precision	square of the correlation coefficient
regr_slope(Y, X)	double precision	double precision	slope of the least-squares-fit linear equation determined by the (X, Y) pairs
regr_sxx(Y, X)	double precision	double precision	sum(X^2) - sum(X)^2/N ("sum of squares" of the independent variable)
regr_sxy(Y, X)	double precision	double precision	sum(XY) - sum(X) sum(Y)/N ("sum of products" of independent times dependent variable)
regr_syy(Y, X)	double precision	double precision	sum(Y^2) - sum(Y)^2/N ("sum of squares" of the dependent variable)
stddev(expression)	smallint, int, bigint, real, double precision, or numeric	double precision for floating-point arguments, otherwise numeric	historical alias for stddev_samp
stddev_pop(expression)	smallint, int, bigint, real, double precision, or numeric	double precision for floating-point arguments, otherwise numeric	population standard deviation of the input values
stddev_samp(expression)	smallint, int, bigint, real, double precision, or numeric	double precision for floating-point arguments, otherwise numeric	sample standard deviation of the input values
variance(expression)	smallint, int, bigint, real, double precision, or numeric	double precision for floating-point arguments, otherwise numeric	historical alias for var_samp
var_pop(expression)	smallint, int, bigint, real, double precision, or numeric	double precision for floating-point arguments, otherwise numeric	population variance of the input values (square of the population standard deviation)
var_samp(expression)	smallint, int, bigint, real, double precision, or numeric	double precision for floating-point arguments, otherwise numeric	sample variance of the input values (square of the sample standard deviation)

Table 9-51 shows some aggregate functions that use the ordered-set aggregate syntax. These functions are sometimes referred to as "inverse distribution" functions.