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From: David Fetter <david@fetter.org>
To: Tomas Vondra <tomas.vondra@2ndquadrant.com>
Cc: pgsql-hackers@postgresql.org
Subject: Re: Weighted Stats
Date: Fri, 8 Apr 2016 15:48:07 -0700
Message-ID: <20160408224807.GC15407@fetter.org> (raw)
In-Reply-To: <20160408204756.GA15407@fetter.org>
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On Fri, Apr 08, 2016 at 01:47:56PM -0700, David Fetter wrote:
> Sorry about the delay.  This patch disallows negative weights,
> although it still has that odd difference Jeff found.

Difference corrected.  It turned out that my reference was mistaken on
the calculation.

Cheers,
David.
-- 
David Fetter <david@fetter.org> http://fetter.org/
Phone: +1 415 235 3778  AIM: dfetter666  Yahoo!: dfetter
Skype: davidfetter      XMPP: david.fetter@gmail.com

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diff --git a/doc/src/sgml/func.sgml b/doc/src/sgml/func.sgml
index cb7fe38..ba31d02 100644
--- a/doc/src/sgml/func.sgml
+++ b/doc/src/sgml/func.sgml
@@ -12750,6 +12750,29 @@ NULL baz</literallayout>(3 rows)</entry>
      <row>
       <entry>
        <indexterm>
+        <primary>weighted_average</primary>
+       </indexterm>
+       <indexterm>
+        <primary>weighted_avg</primary>
+       </indexterm>
+       <function>weighted_avg(<replaceable class="parameter">value expression</replaceable>, <replaceable class="parameter">weight expression</replaceable>)</function>
+      </entry>
+      <entry>
+       <type>smallint</type>, <type>int</type>,
+       <type>bigint</type>, <type>real</type>, <type>double
+       precision</type>, <type>numeric</type>, or <type>interval</type>
+      </entry>
+      <entry>
+       <type>numeric</type> for any integer-type argument,
+       <type>double precision</type> for a floating-point argument,
+       otherwise the same as the argument data type
+      </entry>
+      <entry>the average (arithmetic mean) of all input values, weighted by the input weights</entry>
+     </row>
+
+     <row>
+      <entry>
+       <indexterm>
         <primary>bit_and</primary>
        </indexterm>
        <function>bit_and(<replaceable class="parameter">expression</replaceable>)</function>
@@ -13430,6 +13453,29 @@ SELECT xmlagg(x) FROM (SELECT x FROM test ORDER BY y DESC) AS tab;
      <row>
       <entry>
        <indexterm>
+        <primary>weighted standard deviation</primary>
+        <secondary>population</secondary>
+       </indexterm>
+       <indexterm>
+        <primary>weighted_stddev_pop</primary>
+       </indexterm>
+       <function>weighted_stddev_pop(<replaceable class="parameter">value expression</replaceable>, <replaceable class="parameter">weight expression</replaceable>)</function>
+      </entry>
+      <entry>
+       <type>smallint</type>, <type>int</type>,
+       <type>bigint</type>, <type>real</type>, <type>double
+       precision</type>, or <type>numeric</type>
+      </entry>
+      <entry>
+       <type>double precision</type> for floating-point arguments,
+       otherwise <type>numeric</type>
+      </entry>
+      <entry>weighted population standard deviation of the input values</entry>
+     </row>
+
+     <row>
+      <entry>
+       <indexterm>
         <primary>standard deviation</primary>
         <secondary>sample</secondary>
        </indexterm>
@@ -13454,6 +13500,29 @@ SELECT xmlagg(x) FROM (SELECT x FROM test ORDER BY y DESC) AS tab;
      <row>
       <entry>
        <indexterm>
+        <primary>weighted standard deviation</primary>
+        <secondary>sample</secondary>
+       </indexterm>
+       <indexterm>
+        <primary>weighted_stddev_samp</primary>
+       </indexterm>
+       <function>weighted_stddev_samp(<replaceable class="parameter">value expression</replaceable>, <replaceable class="parameter">weight expression</replaceable>)</function>
+      </entry>
+      <entry>
+       <type>smallint</type>, <type>int</type>,
+       <type>bigint</type>, <type>real</type>, <type>double
+       precision</type>, or <type>numeric</type>
+      </entry>
+      <entry>
+       <type>double precision</type> for floating-point arguments,
+       otherwise <type>numeric</type>
+      </entry>
+      <entry>weighted sample standard deviation of the input values</entry>
+     </row>
+
+     <row>
+      <entry>
+       <indexterm>
         <primary>variance</primary>
        </indexterm>
        <function>variance</function>(<replaceable class="parameter">expression</replaceable>)
diff --git a/src/backend/utils/adt/float.c b/src/backend/utils/adt/float.c
index c7c0b58..fe4a5e4 100644
--- a/src/backend/utils/adt/float.c
+++ b/src/backend/utils/adt/float.c
@@ -2405,6 +2405,7 @@ setseed(PG_FUNCTION_ARGS)
  *		float8_accum		- accumulate for AVG(), variance aggregates, etc.
  *		float4_accum		- same, but input data is float4
  *		float8_avg			- produce final result for float AVG()
+ *		float8_weighted_avg	- produce final result for float WEIGHTED_AVG()
  *		float8_var_samp		- produce final result for float VAR_SAMP()
  *		float8_var_pop		- produce final result for float VAR_POP()
  *		float8_stddev_samp	- produce final result for float STDDEV_SAMP()
@@ -3205,6 +3206,163 @@ float8_regr_intercept(PG_FUNCTION_ARGS)
 	PG_RETURN_FLOAT8(numeratorXXY / numeratorX);
 }
 
+/*
+ *		===================
+ *		WEIGHTED AGGREGATES
+ *		===================
+ *
+ * The transition datatype for these aggregates is a 5-element array
+ * of float8, holding the values N, sum(W), sum(W*X), and sum(W*X*X)
+ * in that order.
+ *
+ * First, an accumulator function for those we can't pirate from the
+ * other accumulators.  This accumulator function takes out some of
+ * the rounding error inherent in the general one.
+ * https://en.wikipedia.org/wiki/Standard_deviation#Rapid_calculation_methods
+ *
+ * It consists of a five-element array which includes:
+ *
+ * N, the number of non-zero-weighted values seen thus far,
+ * W, the running sum of weights,
+ * WX, the running dot product of weights and values,
+ * A, an intermediate value used in the calculation, and
+ * Q, another intermediate value.
+ *
+ */
+
+Datum
+float8_weighted_accum(PG_FUNCTION_ARGS)
+{
+	ArrayType  *transarray = PG_GETARG_ARRAYTYPE_P(0);
+	float8		newvalX = PG_GETARG_FLOAT8(1);
+	float8		newvalW = PG_GETARG_FLOAT8(2);
+	float8	   *transvalues;
+	float8		N,	/* common */
+				W,	/* common */
+				WX,	/* Used in avg */
+				A,	/* Used in stddev_* */
+				Q;	/* Used in stddev_* */
+
+	transvalues = check_float8_array(transarray, "float8_weighted_accum", 5);
+
+	if (newvalW == 0.0) /* Discard zero weights */
+		PG_RETURN_NULL();
+
+	if (newvalW < 0.0) /* Negative weights are an error. */
+		ereport(ERROR,
+				(errmsg("negative weights are not allowed")));
+
+	N  = transvalues[0];
+	W  = transvalues[1];
+	WX = transvalues[2];
+	A  = transvalues[3];
+	Q  = transvalues[4];
+
+	N += 1.0;
+	CHECKFLOATVAL(N, isinf(transvalues[0]), true);
+	W += newvalW;
+	CHECKFLOATVAL(W, isinf(transvalues[1]) || isinf(newvalW), true);
+	WX += newvalW * newvalX;
+	CHECKFLOATVAL(WX, isinf(transvalues[1]) || isinf(newvalW), true);
+	A += newvalW * ( newvalX - transvalues[3] ) / W;
+	CHECKFLOATVAL(A, isinf(newvalW) || isinf(transvalues[3]) || isinf(1.0/W), true);
+	Q += newvalW * (newvalX - transvalues[3]) * (newvalX - A);
+	CHECKFLOATVAL(A, isinf(newvalX -  transvalues[4]) || isinf(newvalX - A) || isinf(1.0/W), true);
+
+	if (AggCheckCallContext(fcinfo, NULL)) /* Update in place is safe in Agg context */
+	{
+		transvalues[0] = N;
+		transvalues[1] = W;
+		transvalues[2] = WX;
+		transvalues[3] = A;
+		transvalues[4] = Q;
+
+		PG_RETURN_ARRAYTYPE_P(transarray);
+	}
+	else /* You do not need to call this directly. */
+		ereport(ERROR,
+				(errmsg("float8_weighted_accum called outside agg context")));
+}
+
+/*
+ * This is the final function for the weighted mean. It uses the
+ * 5-element accumulator common to weighted aggregates.
+ *
+ *     N, the number of elements with non-zero weights,
+ *     sumW, the sum of the weights, and
+ *     sumWX, the dot product of elements and weights.
+ *
+ *  While it might be possible to optimize this further by making a
+ *  more compact accumulator, the performance gain is likely marginal.
+ *
+ */
+Datum
+float8_weighted_avg(PG_FUNCTION_ARGS)
+{
+	ArrayType  *transarray = PG_GETARG_ARRAYTYPE_P(0);
+	float8	   *transvalues;
+	float8		N,
+				sumWX,
+				sumW;
+
+	transvalues = check_float8_array(transarray, "float8_weighted_avg", 5);
+	N = transvalues[0];
+	sumW = transvalues[1];
+	sumWX = transvalues[2];
+
+	if (N < 1.0)
+		PG_RETURN_NULL();
+
+	CHECKFLOATVAL(N, isinf(1.0/sumW) || isinf(sumWX), true);
+
+	PG_RETURN_FLOAT8(sumWX/sumW);
+}
+
+Datum
+float8_weighted_stddev_samp(PG_FUNCTION_ARGS)
+{
+	ArrayType  *transarray = PG_GETARG_ARRAYTYPE_P(0);
+	float8	   *transvalues;
+	float8		N,
+				W,
+				/* Skip A.  Not used in the calculation */
+				Q;
+
+	transvalues = check_float8_array(transarray, "float8_weighted_stddev_samp", 5);
+	N = transvalues[0];
+	W = transvalues[1];
+	Q = transvalues[4];
+
+	if (N < 2.0) /* Must have at least two samples to get a stddev */
+		PG_RETURN_NULL();
+
+	PG_RETURN_FLOAT8(
+		sqrt(
+			Q / (W - 1)
+		)
+	);
+}
+
+Datum
+float8_weighted_stddev_pop(PG_FUNCTION_ARGS)
+{
+	ArrayType  *transarray = PG_GETARG_ARRAYTYPE_P(0);
+	float8	   *transvalues;
+	float8		N,
+				W,
+				/* Skip A.  Not used in the calculation */
+				Q;
+
+	transvalues = check_float8_array(transarray, "float8_weighted_stddev_pop", 5);
+	N = transvalues[0];
+	W = transvalues[1];
+	Q = transvalues[4];
+
+	if (N < 2.0) /* Must have at least two samples to get a stddev */
+		PG_RETURN_NULL();
+
+	PG_RETURN_FLOAT8( sqrt( Q / W ) );
+}
 
 /*
  *		====================================
diff --git a/src/include/catalog/pg_aggregate.h b/src/include/catalog/pg_aggregate.h
index e16aa48..8e2a3a3 100644
--- a/src/include/catalog/pg_aggregate.h
+++ b/src/include/catalog/pg_aggregate.h
@@ -145,6 +145,7 @@ DATA(insert ( 2103	n 0 numeric_avg_accum	numeric_avg			numeric_avg_combine	numer
 DATA(insert ( 2104	n 0 float4_accum		float8_avg			float8_combine		-						-						-				-				-						f f 0	1022	0	0	0		0	"{0,0,0}" _null_ ));
 DATA(insert ( 2105	n 0 float8_accum		float8_avg			float8_combine		-						-						-				-				-						f f 0	1022	0	0	0		0	"{0,0,0}" _null_ ));
 DATA(insert ( 2106	n 0 interval_accum		interval_avg		interval_combine	-						-						interval_accum	interval_accum_inv	interval_avg		f f 0	1187	0	0	1187	0	"{0 second,0 second}" "{0 second,0 second}" ));
+DATA(insert ( 3998 n 0 float8_weighted_accum float8_weighted_avg - - - - - - f f 0 1022 0 40 0 0 "{0,0,0,0,0}" _null_));
 
 /* sum */
 DATA(insert ( 2107	n 0 int8_avg_accum		numeric_poly_sum	int8_avg_combine	int8_avg_serialize		int8_avg_deserialize	int8_avg_accum	int8_avg_accum_inv	numeric_poly_sum	f f 0	2281	17	48	2281	48	_null_ _null_ ));
@@ -237,6 +238,7 @@ DATA(insert ( 2726	n 0 int2_accum		numeric_poly_stddev_pop	numeric_poly_combine
 DATA(insert ( 2727	n 0 float4_accum	float8_stddev_pop		float8_combine			-						-							-				-				-						f f 0	1022	0	0	0		0	"{0,0,0}" _null_ ));
 DATA(insert ( 2728	n 0 float8_accum	float8_stddev_pop		float8_combine			-						-							-				-				-						f f 0	1022	0	0	0		0	"{0,0,0}" _null_ ));
 DATA(insert ( 2729	n 0 numeric_accum	numeric_stddev_pop		numeric_combine			numeric_serialize		numeric_deserialize			numeric_accum	numeric_accum_inv numeric_stddev_pop	f f 0	2281	17	128 2281	128 _null_ _null_ ));
+DATA(insert ( 4032 n 0 float8_weighted_accum float8_weighted_stddev_pop - - - - - - f f 0 1022 0 40 0 0 "{0,0,0,0,0}" _null_));
 
 /* stddev_samp */
 DATA(insert ( 2712	n 0 int8_accum		numeric_stddev_samp			numeric_combine			numeric_serialize		numeric_deserialize			int8_accum	int8_accum_inv	numeric_stddev_samp			f f 0	2281	17	128 2281	128 _null_ _null_ ));
@@ -245,6 +247,7 @@ DATA(insert ( 2714	n 0 int2_accum		numeric_poly_stddev_samp	numeric_poly_combine
 DATA(insert ( 2715	n 0 float4_accum	float8_stddev_samp			float8_combine			-						-							-			-				-							f f 0	1022	0	0	0		0	"{0,0,0}" _null_ ));
 DATA(insert ( 2716	n 0 float8_accum	float8_stddev_samp			float8_combine			-						-							-			-				-							f f 0	1022	0	0	0		0	"{0,0,0}" _null_ ));
 DATA(insert ( 2717	n 0 numeric_accum	numeric_stddev_samp			numeric_combine			numeric_serialize		numeric_deserialize			numeric_accum numeric_accum_inv numeric_stddev_samp		f f 0	2281	17	128 2281	128 _null_ _null_ ));
+DATA(insert ( 4101 n 0 float8_weighted_accum float8_weighted_stddev_samp - - - - - - f f 0 1022 0 40 0 0 "{0,0,0,0,0}" _null_));
 
 /* stddev: historical Postgres syntax for stddev_samp */
 DATA(insert ( 2154	n 0 int8_accum		numeric_stddev_samp			numeric_combine			numeric_serialize		numeric_deserialize			int8_accum		int8_accum_inv	numeric_stddev_samp			f f 0	2281	17	128 2281	128 _null_ _null_ ));
diff --git a/src/include/catalog/pg_proc.h b/src/include/catalog/pg_proc.h
index bb539d4..7dff0d3 100644
--- a/src/include/catalog/pg_proc.h
+++ b/src/include/catalog/pg_proc.h
@@ -2433,6 +2433,12 @@ DESCR("join selectivity of case-insensitive regex non-match");
 /* Aggregate-related functions */
 DATA(insert OID = 1830 (  float8_avg	   PGNSP PGUID 12 1 0 0 0 f f f f t f i s 1 0 701 "1022" _null_ _null_ _null_ _null_ _null_ float8_avg _null_ _null_ _null_ ));
 DESCR("aggregate final function");
+DATA(insert OID = 3997 (  float8_weighted_avg			PGNSP PGUID 12 1 0 0 0 f f f f t f i s 1 0 701 "1022" _null_ _null_ _null_ _null_ _null_ float8_weighted_avg _null_ _null_ _null_ ));
+DESCR("aggregate final function");
+DATA(insert OID = 4099 (  float8_weighted_stddev_pop			PGNSP PGUID 12 1 0 0 0 f f f f t f i s 1 0 701 "1022" _null_ _null_ _null_ _null_ _null_ float8_weighted_stddev_pop _null_ _null_ _null_ ));
+DESCR("aggregate final function");
+DATA(insert OID = 4100 (  float8_weighted_stddev_samp			PGNSP PGUID 12 1 0 0 0 f f f f t f i s 1 0 701 "1022" _null_ _null_ _null_ _null_ _null_ float8_weighted_stddev_samp _null_ _null_ _null_ ));
+DESCR("aggregate final function");
 DATA(insert OID = 2512 (  float8_var_pop   PGNSP PGUID 12 1 0 0 0 f f f f t f i s 1 0 701 "1022" _null_ _null_ _null_ _null_ _null_ float8_var_pop _null_ _null_ _null_ ));
 DESCR("aggregate final function");
 DATA(insert OID = 1831 (  float8_var_samp  PGNSP PGUID 12 1 0 0 0 f f f f t f i s 1 0 701 "1022" _null_ _null_ _null_ _null_ _null_ float8_var_samp _null_ _null_ _null_ ));
@@ -2544,6 +2550,8 @@ DATA(insert OID = 2805 (  int8inc_float8_float8		PGNSP PGUID 12 1 0 0 0 f f f f
 DESCR("aggregate transition function");
 DATA(insert OID = 2806 (  float8_regr_accum			PGNSP PGUID 12 1 0 0 0 f f f f t f i s 3 0 1022 "1022 701 701" _null_ _null_ _null_ _null_ _null_ float8_regr_accum _null_ _null_ _null_ ));
 DESCR("aggregate transition function");
+DATA(insert OID = 3999 (  float8_weighted_accum			PGNSP PGUID 12 1 0 0 0 f f f f t f i s 3 0 1022 "1022 701 701" _null_ _null_ _null_ _null_ _null_ float8_weighted_accum _null_ _null_ _null_ ));
+DESCR("aggregate transition function");
 DATA(insert OID = 3342 (  float8_regr_combine		PGNSP PGUID 12 1 0 0 0 f f f f t f i s 2 0 1022 "1022 1022" _null_ _null_ _null_ _null_ _null_ float8_regr_combine _null_ _null_ _null_ ));
 DESCR("aggregate combine function");
 DATA(insert OID = 2807 (  float8_regr_sxx			PGNSP PGUID 12 1 0 0 0 f f f f t f i s 1 0 701 "1022" _null_ _null_ _null_ _null_ _null_ float8_regr_sxx _null_ _null_ _null_ ));
@@ -3204,6 +3212,8 @@ DATA(insert OID = 2104 (  avg				PGNSP PGUID 12 1 0 0 0 t f f f f f i s 1 0 701
 DESCR("the average (arithmetic mean) as float8 of all float4 values");
 DATA(insert OID = 2105 (  avg				PGNSP PGUID 12 1 0 0 0 t f f f f f i s 1 0 701 "701" _null_ _null_ _null_ _null_ _null_	aggregate_dummy _null_ _null_ _null_ ));
 DESCR("the average (arithmetic mean) as float8 of all float8 values");
+DATA(insert OID = 3998 (  weighted_avg		PGNSP PGUID 12 1 0 0 0 t f f f f f i s 2 0 701 "701 701" _null_ _null_ _null_ _null_ _null_	aggregate_dummy _null_ _null_ _null_ ));
+DESCR("the weighted average (arithmetic mean) as float8 of all float8 values");
 DATA(insert OID = 2106 (  avg				PGNSP PGUID 12 1 0 0 0 t f f f f f i s 1 0 1186 "1186" _null_ _null_ _null_ _null_ _null_ aggregate_dummy _null_ _null_ _null_ ));
 DESCR("the average (arithmetic mean) as interval of all interval values");
 
@@ -3364,6 +3374,8 @@ DATA(insert OID = 2728 (  stddev_pop		PGNSP PGUID 12 1 0 0 0 t f f f f f i s 1 0
 DESCR("population standard deviation of float8 input values");
 DATA(insert OID = 2729 (  stddev_pop		PGNSP PGUID 12 1 0 0 0 t f f f f f i s 1 0 1700 "1700" _null_ _null_ _null_ _null_ _null_ aggregate_dummy _null_ _null_ _null_ ));
 DESCR("population standard deviation of numeric input values");
+DATA(insert OID = 4032 (  weighted_stddev_pop		PGNSP PGUID 12 1 0 0 0 t f f f f f i s 2 0 701 "701 701" _null_ _null_ _null_ _null_ _null_	aggregate_dummy _null_ _null_ _null_ ));
+DESCR("population weighted standard deviation of float8 input values");
 
 DATA(insert OID = 2712 (  stddev_samp		PGNSP PGUID 12 1 0 0 0 t f f f f f i s 1 0 1700 "20" _null_ _null_ _null_ _null_ _null_	aggregate_dummy _null_ _null_ _null_ ));
 DESCR("sample standard deviation of bigint input values");
@@ -3377,6 +3389,8 @@ DATA(insert OID = 2716 (  stddev_samp		PGNSP PGUID 12 1 0 0 0 t f f f f f i s 1
 DESCR("sample standard deviation of float8 input values");
 DATA(insert OID = 2717 (  stddev_samp		PGNSP PGUID 12 1 0 0 0 t f f f f f i s 1 0 1700 "1700" _null_ _null_ _null_ _null_ _null_ aggregate_dummy _null_ _null_ _null_ ));
 DESCR("sample standard deviation of numeric input values");
+DATA(insert OID = 4101 (  weighted_stddev_samp		PGNSP PGUID 12 1 0 0 0 t f f f f f i s 2 0 701 "701 701" _null_ _null_ _null_ _null_ _null_	aggregate_dummy _null_ _null_ _null_ ));
+DESCR("sample weighted standard deviation of float8 input values");
 
 DATA(insert OID = 2154 (  stddev			PGNSP PGUID 12 1 0 0 0 t f f f f f i s 1 0 1700 "20" _null_ _null_ _null_ _null_ _null_	aggregate_dummy _null_ _null_ _null_ ));
 DESCR("historical alias for stddev_samp");
diff --git a/src/include/utils/builtins.h b/src/include/utils/builtins.h
index 01976a1..1c1d0d4 100644
--- a/src/include/utils/builtins.h
+++ b/src/include/utils/builtins.h
@@ -429,8 +429,12 @@ extern Datum drandom(PG_FUNCTION_ARGS);
 extern Datum setseed(PG_FUNCTION_ARGS);
 extern Datum float8_combine(PG_FUNCTION_ARGS);
 extern Datum float8_accum(PG_FUNCTION_ARGS);
+extern Datum float8_weighted_accum(PG_FUNCTION_ARGS);
 extern Datum float4_accum(PG_FUNCTION_ARGS);
 extern Datum float8_avg(PG_FUNCTION_ARGS);
+extern Datum float8_weighted_avg(PG_FUNCTION_ARGS);
+extern Datum float8_weighted_stddev_pop(PG_FUNCTION_ARGS);
+extern Datum float8_weighted_stddev_samp(PG_FUNCTION_ARGS);
 extern Datum float8_var_pop(PG_FUNCTION_ARGS);
 extern Datum float8_var_samp(PG_FUNCTION_ARGS);
 extern Datum float8_stddev_pop(PG_FUNCTION_ARGS);
diff --git a/src/test/regress/expected/aggregates.out b/src/test/regress/expected/aggregates.out
index 3ff6691..c12ea3b 100644
--- a/src/test/regress/expected/aggregates.out
+++ b/src/test/regress/expected/aggregates.out
@@ -247,6 +247,18 @@ SELECT covar_pop(b, a), covar_samp(b, a) FROM aggtest;
  653.62895538751 | 871.505273850014
 (1 row)
 
+SELECT weighted_avg(a, b) FROM aggtest;
+   weighted_avg   
+------------------
+ 55.5553072763149
+(1 row)
+
+SELECT weighted_stddev_pop(a, b), weighted_stddev_samp(a, b) FROM aggtest;
+ weighted_stddev_pop | weighted_stddev_samp 
+---------------------+----------------------
+    24.3364627240769 |     28.1013266097382
+(1 row)
+
 SELECT corr(b, a) FROM aggtest;
        corr        
 -------------------
diff --git a/src/test/regress/sql/aggregates.sql b/src/test/regress/sql/aggregates.sql
index 80ef14c..6f236a1 100644
--- a/src/test/regress/sql/aggregates.sql
+++ b/src/test/regress/sql/aggregates.sql
@@ -60,6 +60,8 @@ SELECT regr_avgx(b, a), regr_avgy(b, a) FROM aggtest;
 SELECT regr_r2(b, a) FROM aggtest;
 SELECT regr_slope(b, a), regr_intercept(b, a) FROM aggtest;
 SELECT covar_pop(b, a), covar_samp(b, a) FROM aggtest;
+SELECT weighted_avg(a, b) FROM aggtest;
+SELECT weighted_stddev_pop(a, b), weighted_stddev_samp(a, b) FROM aggtest;
 SELECT corr(b, a) FROM aggtest;
 
 SELECT count(four) AS cnt_1000 FROM onek;

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Attachments:

weighted_stats_004.diff (text/plain, 19.0K) download
diff --git a/doc/src/sgml/func.sgml b/doc/src/sgml/func.sgml
index cb7fe38..ba31d02 100644
--- a/doc/src/sgml/func.sgml
+++ b/doc/src/sgml/func.sgml
@@ -12750,6 +12750,29 @@ NULL baz</literallayout>(3 rows)</entry>
      <row>
       <entry>
        <indexterm>
+        <primary>weighted_average</primary>
+       </indexterm>
+       <indexterm>
+        <primary>weighted_avg</primary>
+       </indexterm>
+       <function>weighted_avg(<replaceable class="parameter">value expression</replaceable>, <replaceable class="parameter">weight expression</replaceable>)</function>
+      </entry>
+      <entry>
+       <type>smallint</type>, <type>int</type>,
+       <type>bigint</type>, <type>real</type>, <type>double
+       precision</type>, <type>numeric</type>, or <type>interval</type>
+      </entry>
+      <entry>
+       <type>numeric</type> for any integer-type argument,
+       <type>double precision</type> for a floating-point argument,
+       otherwise the same as the argument data type
+      </entry>
+      <entry>the average (arithmetic mean) of all input values, weighted by the input weights</entry>
+     </row>
+
+     <row>
+      <entry>
+       <indexterm>
         <primary>bit_and</primary>
        </indexterm>
        <function>bit_and(<replaceable class="parameter">expression</replaceable>)</function>
@@ -13430,6 +13453,29 @@ SELECT xmlagg(x) FROM (SELECT x FROM test ORDER BY y DESC) AS tab;
      <row>
       <entry>
        <indexterm>
+        <primary>weighted standard deviation</primary>
+        <secondary>population</secondary>
+       </indexterm>
+       <indexterm>
+        <primary>weighted_stddev_pop</primary>
+       </indexterm>
+       <function>weighted_stddev_pop(<replaceable class="parameter">value expression</replaceable>, <replaceable class="parameter">weight expression</replaceable>)</function>
+      </entry>
+      <entry>
+       <type>smallint</type>, <type>int</type>,
+       <type>bigint</type>, <type>real</type>, <type>double
+       precision</type>, or <type>numeric</type>
+      </entry>
+      <entry>
+       <type>double precision</type> for floating-point arguments,
+       otherwise <type>numeric</type>
+      </entry>
+      <entry>weighted population standard deviation of the input values</entry>
+     </row>
+
+     <row>
+      <entry>
+       <indexterm>
         <primary>standard deviation</primary>
         <secondary>sample</secondary>
        </indexterm>
@@ -13454,6 +13500,29 @@ SELECT xmlagg(x) FROM (SELECT x FROM test ORDER BY y DESC) AS tab;
      <row>
       <entry>
        <indexterm>
+        <primary>weighted standard deviation</primary>
+        <secondary>sample</secondary>
+       </indexterm>
+       <indexterm>
+        <primary>weighted_stddev_samp</primary>
+       </indexterm>
+       <function>weighted_stddev_samp(<replaceable class="parameter">value expression</replaceable>, <replaceable class="parameter">weight expression</replaceable>)</function>
+      </entry>
+      <entry>
+       <type>smallint</type>, <type>int</type>,
+       <type>bigint</type>, <type>real</type>, <type>double
+       precision</type>, or <type>numeric</type>
+      </entry>
+      <entry>
+       <type>double precision</type> for floating-point arguments,
+       otherwise <type>numeric</type>
+      </entry>
+      <entry>weighted sample standard deviation of the input values</entry>
+     </row>
+
+     <row>
+      <entry>
+       <indexterm>
         <primary>variance</primary>
        </indexterm>
        <function>variance</function>(<replaceable class="parameter">expression</replaceable>)
diff --git a/src/backend/utils/adt/float.c b/src/backend/utils/adt/float.c
index c7c0b58..fe4a5e4 100644
--- a/src/backend/utils/adt/float.c
+++ b/src/backend/utils/adt/float.c
@@ -2405,6 +2405,7 @@ setseed(PG_FUNCTION_ARGS)
  *		float8_accum		- accumulate for AVG(), variance aggregates, etc.
  *		float4_accum		- same, but input data is float4
  *		float8_avg			- produce final result for float AVG()
+ *		float8_weighted_avg	- produce final result for float WEIGHTED_AVG()
  *		float8_var_samp		- produce final result for float VAR_SAMP()
  *		float8_var_pop		- produce final result for float VAR_POP()
  *		float8_stddev_samp	- produce final result for float STDDEV_SAMP()
@@ -3205,6 +3206,163 @@ float8_regr_intercept(PG_FUNCTION_ARGS)
 	PG_RETURN_FLOAT8(numeratorXXY / numeratorX);
 }
 
+/*
+ *		===================
+ *		WEIGHTED AGGREGATES
+ *		===================
+ *
+ * The transition datatype for these aggregates is a 5-element array
+ * of float8, holding the values N, sum(W), sum(W*X), and sum(W*X*X)
+ * in that order.
+ *
+ * First, an accumulator function for those we can't pirate from the
+ * other accumulators.  This accumulator function takes out some of
+ * the rounding error inherent in the general one.
+ * https://en.wikipedia.org/wiki/Standard_deviation#Rapid_calculation_methods
+ *
+ * It consists of a five-element array which includes:
+ *
+ * N, the number of non-zero-weighted values seen thus far,
+ * W, the running sum of weights,
+ * WX, the running dot product of weights and values,
+ * A, an intermediate value used in the calculation, and
+ * Q, another intermediate value.
+ *
+ */
+
+Datum
+float8_weighted_accum(PG_FUNCTION_ARGS)
+{
+	ArrayType  *transarray = PG_GETARG_ARRAYTYPE_P(0);
+	float8		newvalX = PG_GETARG_FLOAT8(1);
+	float8		newvalW = PG_GETARG_FLOAT8(2);
+	float8	   *transvalues;
+	float8		N,	/* common */
+				W,	/* common */
+				WX,	/* Used in avg */
+				A,	/* Used in stddev_* */
+				Q;	/* Used in stddev_* */
+
+	transvalues = check_float8_array(transarray, "float8_weighted_accum", 5);
+
+	if (newvalW == 0.0) /* Discard zero weights */
+		PG_RETURN_NULL();
+
+	if (newvalW < 0.0) /* Negative weights are an error. */
+		ereport(ERROR,
+				(errmsg("negative weights are not allowed")));
+
+	N  = transvalues[0];
+	W  = transvalues[1];
+	WX = transvalues[2];
+	A  = transvalues[3];
+	Q  = transvalues[4];
+
+	N += 1.0;
+	CHECKFLOATVAL(N, isinf(transvalues[0]), true);
+	W += newvalW;
+	CHECKFLOATVAL(W, isinf(transvalues[1]) || isinf(newvalW), true);
+	WX += newvalW * newvalX;
+	CHECKFLOATVAL(WX, isinf(transvalues[1]) || isinf(newvalW), true);
+	A += newvalW * ( newvalX - transvalues[3] ) / W;
+	CHECKFLOATVAL(A, isinf(newvalW) || isinf(transvalues[3]) || isinf(1.0/W), true);
+	Q += newvalW * (newvalX - transvalues[3]) * (newvalX - A);
+	CHECKFLOATVAL(A, isinf(newvalX -  transvalues[4]) || isinf(newvalX - A) || isinf(1.0/W), true);
+
+	if (AggCheckCallContext(fcinfo, NULL)) /* Update in place is safe in Agg context */
+	{
+		transvalues[0] = N;
+		transvalues[1] = W;
+		transvalues[2] = WX;
+		transvalues[3] = A;
+		transvalues[4] = Q;
+
+		PG_RETURN_ARRAYTYPE_P(transarray);
+	}
+	else /* You do not need to call this directly. */
+		ereport(ERROR,
+				(errmsg("float8_weighted_accum called outside agg context")));
+}
+
+/*
+ * This is the final function for the weighted mean. It uses the
+ * 5-element accumulator common to weighted aggregates.
+ *
+ *     N, the number of elements with non-zero weights,
+ *     sumW, the sum of the weights, and
+ *     sumWX, the dot product of elements and weights.
+ *
+ *  While it might be possible to optimize this further by making a
+ *  more compact accumulator, the performance gain is likely marginal.
+ *
+ */
+Datum
+float8_weighted_avg(PG_FUNCTION_ARGS)
+{
+	ArrayType  *transarray = PG_GETARG_ARRAYTYPE_P(0);
+	float8	   *transvalues;
+	float8		N,
+				sumWX,
+				sumW;
+
+	transvalues = check_float8_array(transarray, "float8_weighted_avg", 5);
+	N = transvalues[0];
+	sumW = transvalues[1];
+	sumWX = transvalues[2];
+
+	if (N < 1.0)
+		PG_RETURN_NULL();
+
+	CHECKFLOATVAL(N, isinf(1.0/sumW) || isinf(sumWX), true);
+
+	PG_RETURN_FLOAT8(sumWX/sumW);
+}
+
+Datum
+float8_weighted_stddev_samp(PG_FUNCTION_ARGS)
+{
+	ArrayType  *transarray = PG_GETARG_ARRAYTYPE_P(0);
+	float8	   *transvalues;
+	float8		N,
+				W,
+				/* Skip A.  Not used in the calculation */
+				Q;
+
+	transvalues = check_float8_array(transarray, "float8_weighted_stddev_samp", 5);
+	N = transvalues[0];
+	W = transvalues[1];
+	Q = transvalues[4];
+
+	if (N < 2.0) /* Must have at least two samples to get a stddev */
+		PG_RETURN_NULL();
+
+	PG_RETURN_FLOAT8(
+		sqrt(
+			Q / (W - 1)
+		)
+	);
+}
+
+Datum
+float8_weighted_stddev_pop(PG_FUNCTION_ARGS)
+{
+	ArrayType  *transarray = PG_GETARG_ARRAYTYPE_P(0);
+	float8	   *transvalues;
+	float8		N,
+				W,
+				/* Skip A.  Not used in the calculation */
+				Q;
+
+	transvalues = check_float8_array(transarray, "float8_weighted_stddev_pop", 5);
+	N = transvalues[0];
+	W = transvalues[1];
+	Q = transvalues[4];
+
+	if (N < 2.0) /* Must have at least two samples to get a stddev */
+		PG_RETURN_NULL();
+
+	PG_RETURN_FLOAT8( sqrt( Q / W ) );
+}
 
 /*
  *		====================================
diff --git a/src/include/catalog/pg_aggregate.h b/src/include/catalog/pg_aggregate.h
index e16aa48..8e2a3a3 100644
--- a/src/include/catalog/pg_aggregate.h
+++ b/src/include/catalog/pg_aggregate.h
@@ -145,6 +145,7 @@ DATA(insert ( 2103	n 0 numeric_avg_accum	numeric_avg			numeric_avg_combine	numer
 DATA(insert ( 2104	n 0 float4_accum		float8_avg			float8_combine		-						-						-				-				-						f f 0	1022	0	0	0		0	"{0,0,0}" _null_ ));
 DATA(insert ( 2105	n 0 float8_accum		float8_avg			float8_combine		-						-						-				-				-						f f 0	1022	0	0	0		0	"{0,0,0}" _null_ ));
 DATA(insert ( 2106	n 0 interval_accum		interval_avg		interval_combine	-						-						interval_accum	interval_accum_inv	interval_avg		f f 0	1187	0	0	1187	0	"{0 second,0 second}" "{0 second,0 second}" ));
+DATA(insert ( 3998 n 0 float8_weighted_accum float8_weighted_avg - - - - - - f f 0 1022 0 40 0 0 "{0,0,0,0,0}" _null_));
 
 /* sum */
 DATA(insert ( 2107	n 0 int8_avg_accum		numeric_poly_sum	int8_avg_combine	int8_avg_serialize		int8_avg_deserialize	int8_avg_accum	int8_avg_accum_inv	numeric_poly_sum	f f 0	2281	17	48	2281	48	_null_ _null_ ));
@@ -237,6 +238,7 @@ DATA(insert ( 2726	n 0 int2_accum		numeric_poly_stddev_pop	numeric_poly_combine
 DATA(insert ( 2727	n 0 float4_accum	float8_stddev_pop		float8_combine			-						-							-				-				-						f f 0	1022	0	0	0		0	"{0,0,0}" _null_ ));
 DATA(insert ( 2728	n 0 float8_accum	float8_stddev_pop		float8_combine			-						-							-				-				-						f f 0	1022	0	0	0		0	"{0,0,0}" _null_ ));
 DATA(insert ( 2729	n 0 numeric_accum	numeric_stddev_pop		numeric_combine			numeric_serialize		numeric_deserialize			numeric_accum	numeric_accum_inv numeric_stddev_pop	f f 0	2281	17	128 2281	128 _null_ _null_ ));
+DATA(insert ( 4032 n 0 float8_weighted_accum float8_weighted_stddev_pop - - - - - - f f 0 1022 0 40 0 0 "{0,0,0,0,0}" _null_));
 
 /* stddev_samp */
 DATA(insert ( 2712	n 0 int8_accum		numeric_stddev_samp			numeric_combine			numeric_serialize		numeric_deserialize			int8_accum	int8_accum_inv	numeric_stddev_samp			f f 0	2281	17	128 2281	128 _null_ _null_ ));
@@ -245,6 +247,7 @@ DATA(insert ( 2714	n 0 int2_accum		numeric_poly_stddev_samp	numeric_poly_combine
 DATA(insert ( 2715	n 0 float4_accum	float8_stddev_samp			float8_combine			-						-							-			-				-							f f 0	1022	0	0	0		0	"{0,0,0}" _null_ ));
 DATA(insert ( 2716	n 0 float8_accum	float8_stddev_samp			float8_combine			-						-							-			-				-							f f 0	1022	0	0	0		0	"{0,0,0}" _null_ ));
 DATA(insert ( 2717	n 0 numeric_accum	numeric_stddev_samp			numeric_combine			numeric_serialize		numeric_deserialize			numeric_accum numeric_accum_inv numeric_stddev_samp		f f 0	2281	17	128 2281	128 _null_ _null_ ));
+DATA(insert ( 4101 n 0 float8_weighted_accum float8_weighted_stddev_samp - - - - - - f f 0 1022 0 40 0 0 "{0,0,0,0,0}" _null_));
 
 /* stddev: historical Postgres syntax for stddev_samp */
 DATA(insert ( 2154	n 0 int8_accum		numeric_stddev_samp			numeric_combine			numeric_serialize		numeric_deserialize			int8_accum		int8_accum_inv	numeric_stddev_samp			f f 0	2281	17	128 2281	128 _null_ _null_ ));
diff --git a/src/include/catalog/pg_proc.h b/src/include/catalog/pg_proc.h
index bb539d4..7dff0d3 100644
--- a/src/include/catalog/pg_proc.h
+++ b/src/include/catalog/pg_proc.h
@@ -2433,6 +2433,12 @@ DESCR("join selectivity of case-insensitive regex non-match");
 /* Aggregate-related functions */
 DATA(insert OID = 1830 (  float8_avg	   PGNSP PGUID 12 1 0 0 0 f f f f t f i s 1 0 701 "1022" _null_ _null_ _null_ _null_ _null_ float8_avg _null_ _null_ _null_ ));
 DESCR("aggregate final function");
+DATA(insert OID = 3997 (  float8_weighted_avg			PGNSP PGUID 12 1 0 0 0 f f f f t f i s 1 0 701 "1022" _null_ _null_ _null_ _null_ _null_ float8_weighted_avg _null_ _null_ _null_ ));
+DESCR("aggregate final function");
+DATA(insert OID = 4099 (  float8_weighted_stddev_pop			PGNSP PGUID 12 1 0 0 0 f f f f t f i s 1 0 701 "1022" _null_ _null_ _null_ _null_ _null_ float8_weighted_stddev_pop _null_ _null_ _null_ ));
+DESCR("aggregate final function");
+DATA(insert OID = 4100 (  float8_weighted_stddev_samp			PGNSP PGUID 12 1 0 0 0 f f f f t f i s 1 0 701 "1022" _null_ _null_ _null_ _null_ _null_ float8_weighted_stddev_samp _null_ _null_ _null_ ));
+DESCR("aggregate final function");
 DATA(insert OID = 2512 (  float8_var_pop   PGNSP PGUID 12 1 0 0 0 f f f f t f i s 1 0 701 "1022" _null_ _null_ _null_ _null_ _null_ float8_var_pop _null_ _null_ _null_ ));
 DESCR("aggregate final function");
 DATA(insert OID = 1831 (  float8_var_samp  PGNSP PGUID 12 1 0 0 0 f f f f t f i s 1 0 701 "1022" _null_ _null_ _null_ _null_ _null_ float8_var_samp _null_ _null_ _null_ ));
@@ -2544,6 +2550,8 @@ DATA(insert OID = 2805 (  int8inc_float8_float8		PGNSP PGUID 12 1 0 0 0 f f f f
 DESCR("aggregate transition function");
 DATA(insert OID = 2806 (  float8_regr_accum			PGNSP PGUID 12 1 0 0 0 f f f f t f i s 3 0 1022 "1022 701 701" _null_ _null_ _null_ _null_ _null_ float8_regr_accum _null_ _null_ _null_ ));
 DESCR("aggregate transition function");
+DATA(insert OID = 3999 (  float8_weighted_accum			PGNSP PGUID 12 1 0 0 0 f f f f t f i s 3 0 1022 "1022 701 701" _null_ _null_ _null_ _null_ _null_ float8_weighted_accum _null_ _null_ _null_ ));
+DESCR("aggregate transition function");
 DATA(insert OID = 3342 (  float8_regr_combine		PGNSP PGUID 12 1 0 0 0 f f f f t f i s 2 0 1022 "1022 1022" _null_ _null_ _null_ _null_ _null_ float8_regr_combine _null_ _null_ _null_ ));
 DESCR("aggregate combine function");
 DATA(insert OID = 2807 (  float8_regr_sxx			PGNSP PGUID 12 1 0 0 0 f f f f t f i s 1 0 701 "1022" _null_ _null_ _null_ _null_ _null_ float8_regr_sxx _null_ _null_ _null_ ));
@@ -3204,6 +3212,8 @@ DATA(insert OID = 2104 (  avg				PGNSP PGUID 12 1 0 0 0 t f f f f f i s 1 0 701
 DESCR("the average (arithmetic mean) as float8 of all float4 values");
 DATA(insert OID = 2105 (  avg				PGNSP PGUID 12 1 0 0 0 t f f f f f i s 1 0 701 "701" _null_ _null_ _null_ _null_ _null_	aggregate_dummy _null_ _null_ _null_ ));
 DESCR("the average (arithmetic mean) as float8 of all float8 values");
+DATA(insert OID = 3998 (  weighted_avg		PGNSP PGUID 12 1 0 0 0 t f f f f f i s 2 0 701 "701 701" _null_ _null_ _null_ _null_ _null_	aggregate_dummy _null_ _null_ _null_ ));
+DESCR("the weighted average (arithmetic mean) as float8 of all float8 values");
 DATA(insert OID = 2106 (  avg				PGNSP PGUID 12 1 0 0 0 t f f f f f i s 1 0 1186 "1186" _null_ _null_ _null_ _null_ _null_ aggregate_dummy _null_ _null_ _null_ ));
 DESCR("the average (arithmetic mean) as interval of all interval values");
 
@@ -3364,6 +3374,8 @@ DATA(insert OID = 2728 (  stddev_pop		PGNSP PGUID 12 1 0 0 0 t f f f f f i s 1 0
 DESCR("population standard deviation of float8 input values");
 DATA(insert OID = 2729 (  stddev_pop		PGNSP PGUID 12 1 0 0 0 t f f f f f i s 1 0 1700 "1700" _null_ _null_ _null_ _null_ _null_ aggregate_dummy _null_ _null_ _null_ ));
 DESCR("population standard deviation of numeric input values");
+DATA(insert OID = 4032 (  weighted_stddev_pop		PGNSP PGUID 12 1 0 0 0 t f f f f f i s 2 0 701 "701 701" _null_ _null_ _null_ _null_ _null_	aggregate_dummy _null_ _null_ _null_ ));
+DESCR("population weighted standard deviation of float8 input values");
 
 DATA(insert OID = 2712 (  stddev_samp		PGNSP PGUID 12 1 0 0 0 t f f f f f i s 1 0 1700 "20" _null_ _null_ _null_ _null_ _null_	aggregate_dummy _null_ _null_ _null_ ));
 DESCR("sample standard deviation of bigint input values");
@@ -3377,6 +3389,8 @@ DATA(insert OID = 2716 (  stddev_samp		PGNSP PGUID 12 1 0 0 0 t f f f f f i s 1
 DESCR("sample standard deviation of float8 input values");
 DATA(insert OID = 2717 (  stddev_samp		PGNSP PGUID 12 1 0 0 0 t f f f f f i s 1 0 1700 "1700" _null_ _null_ _null_ _null_ _null_ aggregate_dummy _null_ _null_ _null_ ));
 DESCR("sample standard deviation of numeric input values");
+DATA(insert OID = 4101 (  weighted_stddev_samp		PGNSP PGUID 12 1 0 0 0 t f f f f f i s 2 0 701 "701 701" _null_ _null_ _null_ _null_ _null_	aggregate_dummy _null_ _null_ _null_ ));
+DESCR("sample weighted standard deviation of float8 input values");
 
 DATA(insert OID = 2154 (  stddev			PGNSP PGUID 12 1 0 0 0 t f f f f f i s 1 0 1700 "20" _null_ _null_ _null_ _null_ _null_	aggregate_dummy _null_ _null_ _null_ ));
 DESCR("historical alias for stddev_samp");
diff --git a/src/include/utils/builtins.h b/src/include/utils/builtins.h
index 01976a1..1c1d0d4 100644
--- a/src/include/utils/builtins.h
+++ b/src/include/utils/builtins.h
@@ -429,8 +429,12 @@ extern Datum drandom(PG_FUNCTION_ARGS);
 extern Datum setseed(PG_FUNCTION_ARGS);
 extern Datum float8_combine(PG_FUNCTION_ARGS);
 extern Datum float8_accum(PG_FUNCTION_ARGS);
+extern Datum float8_weighted_accum(PG_FUNCTION_ARGS);
 extern Datum float4_accum(PG_FUNCTION_ARGS);
 extern Datum float8_avg(PG_FUNCTION_ARGS);
+extern Datum float8_weighted_avg(PG_FUNCTION_ARGS);
+extern Datum float8_weighted_stddev_pop(PG_FUNCTION_ARGS);
+extern Datum float8_weighted_stddev_samp(PG_FUNCTION_ARGS);
 extern Datum float8_var_pop(PG_FUNCTION_ARGS);
 extern Datum float8_var_samp(PG_FUNCTION_ARGS);
 extern Datum float8_stddev_pop(PG_FUNCTION_ARGS);
diff --git a/src/test/regress/expected/aggregates.out b/src/test/regress/expected/aggregates.out
index 3ff6691..c12ea3b 100644
--- a/src/test/regress/expected/aggregates.out
+++ b/src/test/regress/expected/aggregates.out
@@ -247,6 +247,18 @@ SELECT covar_pop(b, a), covar_samp(b, a) FROM aggtest;
  653.62895538751 | 871.505273850014
 (1 row)
 
+SELECT weighted_avg(a, b) FROM aggtest;
+   weighted_avg   
+------------------
+ 55.5553072763149
+(1 row)
+
+SELECT weighted_stddev_pop(a, b), weighted_stddev_samp(a, b) FROM aggtest;
+ weighted_stddev_pop | weighted_stddev_samp 
+---------------------+----------------------
+    24.3364627240769 |     28.1013266097382
+(1 row)
+
 SELECT corr(b, a) FROM aggtest;
        corr        
 -------------------
diff --git a/src/test/regress/sql/aggregates.sql b/src/test/regress/sql/aggregates.sql
index 80ef14c..6f236a1 100644
--- a/src/test/regress/sql/aggregates.sql
+++ b/src/test/regress/sql/aggregates.sql
@@ -60,6 +60,8 @@ SELECT regr_avgx(b, a), regr_avgy(b, a) FROM aggtest;
 SELECT regr_r2(b, a) FROM aggtest;
 SELECT regr_slope(b, a), regr_intercept(b, a) FROM aggtest;
 SELECT covar_pop(b, a), covar_samp(b, a) FROM aggtest;
+SELECT weighted_avg(a, b) FROM aggtest;
+SELECT weighted_stddev_pop(a, b), weighted_stddev_samp(a, b) FROM aggtest;
 SELECT corr(b, a) FROM aggtest;
 
 SELECT count(four) AS cnt_1000 FROM onek;

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