PostgreSQL aggregate function 2 : Aggregate Functions for Statistics
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 :
《population & sample covariance, standard deviation Aggregate in PostgreSQL》
《PostgreSQL 统计信息之 - 逻辑与物理存储的线性相关性》
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(X*Y) - 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.
如下 :
相关性统计 :
corr, regr_r2
《PostgreSQL 统计信息之 - 逻辑与物理存储的线性相关性》
| 总体 | 样本 方差, 标准方差 : |
variance, var_pop, var_samp
stddev, stddev_pop, stddev_samp
《population & sample covariance, standard deviation Aggregate in PostgreSQL》
总体协方差, 样本协方差 :
covar_pop, covar_samp
《用PostgreSQL了解一些统计学术语以及计算方法和表示方法 - 1》
线性回归 :
regr_avgx, regr_avgy, regr_count, regr_intercept(截距), regr_r2(相关度corr的平方), regr_slope(斜率), regr_sxx, regr_sxy, regr_syy.
《在PostgreSQL中用线性回归分析(linear regression) - 实现数据预测》
参考
1. http://www.postgresql.org/docs/9.4/static/functions-aggregate.html
2. src/backend/utils/adt/float.c
《PostgreSQL aggregate function 1 : General-Purpose Aggregate Functions》