Fix and add tests

dbms/src/AggregateFunctions/AggregateFunctionStatisticsSimple.h

@@ -189,6 +189,9 @@ struct HighOrderMoments
 
     T NO_SANITIZE_UNDEFINED getMoment3() const
     {
+        // to avoid accuracy problem
+        if (m0 == 1)
+            return 0;
         return (m3
             - (3 * m2
                 - 2 * m1 * m1 / m0
@@ -198,6 +201,9 @@ struct HighOrderMoments
 
     T NO_SANITIZE_UNDEFINED getMoment4() const
     {
+        // to avoid accuracy problem
+        if (m0 == 1)
+            return 0;
         return (m4
             - (4 * m3
                 - (6 * m2

dbms/tests/queries/0_stateless/00181_aggregate_functions_statistics.reference

@@ -5,6 +5,12 @@ nan
 nan
 0
 nan
+nan
+0
+nan
+nan
+0
+nan
 0
 0
 nan
@@ -14,6 +20,12 @@ nan
 nan
 0
 nan
+nan
+0
+nan
+nan
+0
+nan
 0
 0
 nan

dbms/tests/queries/0_stateless/00181_aggregate_functions_statistics.sql

@@ -30,6 +30,41 @@ SELECT
 FROM series
 );
 
+/* skewSamp */
+
+SELECT skewSamp(x_value) FROM (SELECT x_value FROM series LIMIT 0);
+SELECT skewSamp(x_value) FROM (SELECT x_value FROM series LIMIT 1);
+
+SELECT round(abs(res1 - res2), 6) FROM
+(
+SELECT
+    skewSamp(x_value) AS res1,
+    (
+        sum(x_value * x_value * x_value) / count()
+        - 3 * sum(x_value * x_value) / count() * sum(x_value) / count()
+        + 2 * sum(x_value) / count() * sum(x_value) / count() * sum(x_value) / count()
+    ) / pow((sum(x_value * x_value) - ((sum(x_value) * sum(x_value)) / count())) / (count() - 1), 1.5) AS res2
+FROM series
+);
+
+/* kurtSamp */
+
+SELECT kurtSamp(x_value) FROM (SELECT x_value FROM series LIMIT 0);
+SELECT kurtSamp(x_value) FROM (SELECT x_value FROM series LIMIT 1);
+
+SELECT round(abs(res1 - res2), 6) FROM
+(
+SELECT
+    kurtSamp(x_value) AS res1,
+    (
+        sum(x_value * x_value * x_value * x_value) / count()
+        - 4 * sum(x_value * x_value * x_value) / count() * sum(x_value) / count()
+        + 6 * sum(x_value * x_value) / count() * sum(x_value) / count() * sum(x_value) / count()
+        - 3 * sum(x_value) / count() * sum(x_value) / count() * sum(x_value) / count() * sum(x_value) / count()
+    ) / pow((sum(x_value * x_value) - ((sum(x_value) * sum(x_value)) / count())) / (count() - 1), 2) AS res2
+FROM series
+);
+
 /* varPop */
 
 SELECT varPop(x_value) FROM (SELECT x_value FROM series LIMIT 0);
@@ -56,6 +91,41 @@ SELECT
 FROM series
 );
 
+/* skewPop */
+
+SELECT skewPop(x_value) FROM (SELECT x_value FROM series LIMIT 0);
+SELECT skewPop(x_value) FROM (SELECT x_value FROM series LIMIT 1);
+
+SELECT round(abs(res1 - res2), 6) FROM
+(
+SELECT
+    skewPop(x_value) AS res1,
+    (
+        sum(x_value * x_value * x_value) / count()
+        - 3 * sum(x_value * x_value) / count() * sum(x_value) / count()
+        + 2 * sum(x_value) / count() * sum(x_value) / count() * sum(x_value) / count()
+    ) / pow((sum(x_value * x_value) - ((sum(x_value) * sum(x_value)) / count())) / count(), 1.5) AS res2
+FROM series
+);
+
+/* kurtPop */
+
+SELECT kurtPop(x_value) FROM (SELECT x_value FROM series LIMIT 0);
+SELECT kurtPop(x_value) FROM (SELECT x_value FROM series LIMIT 1);
+
+SELECT round(abs(res1 - res2), 6) FROM
+(
+SELECT
+    kurtPop(x_value) AS res1,
+    (
+        sum(x_value * x_value * x_value * x_value) / count()
+        - 4 * sum(x_value * x_value * x_value) / count() * sum(x_value) / count()
+        + 6 * sum(x_value * x_value) / count() * sum(x_value) / count() * sum(x_value) / count()
+        - 3 * sum(x_value) / count() * sum(x_value) / count() * sum(x_value) / count() * sum(x_value) / count()
+    ) / pow((sum(x_value * x_value) - ((sum(x_value) * sum(x_value)) / count())) / count(), 2) AS res2
+FROM series
+);
+
 /* covarSamp */
 
 SELECT covarSamp(x_value, y_value) FROM (SELECT x_value, y_value FROM series LIMIT 0);