diff --git a/external/docker-integration-tests/src/test/scala/org/apache/spark/sql/jdbc/v2/DB2IntegrationSuite.scala b/external/docker-integration-tests/src/test/scala/org/apache/spark/sql/jdbc/v2/DB2IntegrationSuite.scala
index 2cfb21395d8a9..4b2bbbdd8494c 100644
--- a/external/docker-integration-tests/src/test/scala/org/apache/spark/sql/jdbc/v2/DB2IntegrationSuite.scala
+++ b/external/docker-integration-tests/src/test/scala/org/apache/spark/sql/jdbc/v2/DB2IntegrationSuite.scala
@@ -97,4 +97,13 @@ class DB2IntegrationSuite extends DockerJDBCIntegrationV2Suite with V2JDBCTest {
   override def caseConvert(tableName: String): String = tableName.toUpperCase(Locale.ROOT)
 
   testVarPop()
+  testVarPop(true)
+  testVarSamp()
+  testVarSamp(true)
+  testStddevPop()
+  testStddevPop(true)
+  testStddevSamp()
+  testStddevSamp(true)
+  testCovarPop()
+  testCovarSamp()
 }
diff --git a/external/docker-integration-tests/src/test/scala/org/apache/spark/sql/jdbc/v2/MsSqlServerIntegrationSuite.scala b/external/docker-integration-tests/src/test/scala/org/apache/spark/sql/jdbc/v2/MsSqlServerIntegrationSuite.scala
index e9521ec35a8ce..a527c6f8cb5b6 100644
--- a/external/docker-integration-tests/src/test/scala/org/apache/spark/sql/jdbc/v2/MsSqlServerIntegrationSuite.scala
+++ b/external/docker-integration-tests/src/test/scala/org/apache/spark/sql/jdbc/v2/MsSqlServerIntegrationSuite.scala
@@ -98,7 +98,11 @@ class MsSqlServerIntegrationSuite extends DockerJDBCIntegrationV2Suite with V2JD
   }
 
   testVarPop()
+  testVarPop(true)
   testVarSamp()
+  testVarSamp(true)
   testStddevPop()
+  testStddevPop(true)
   testStddevSamp()
+  testStddevSamp(true)
 }
diff --git a/external/docker-integration-tests/src/test/scala/org/apache/spark/sql/jdbc/v2/PostgresIntegrationSuite.scala b/external/docker-integration-tests/src/test/scala/org/apache/spark/sql/jdbc/v2/PostgresIntegrationSuite.scala
index 86f5c3c8cd418..77ace3f3f4ea7 100644
--- a/external/docker-integration-tests/src/test/scala/org/apache/spark/sql/jdbc/v2/PostgresIntegrationSuite.scala
+++ b/external/docker-integration-tests/src/test/scala/org/apache/spark/sql/jdbc/v2/PostgresIntegrationSuite.scala
@@ -91,10 +91,17 @@ class PostgresIntegrationSuite extends DockerJDBCIntegrationV2Suite with V2JDBCT
   override def indexOptions: String = "FILLFACTOR=70"
 
   testVarPop()
+  testVarPop(true)
   testVarSamp()
+  testVarSamp(true)
   testStddevPop()
+  testStddevPop(true)
   testStddevSamp()
+  testStddevSamp(true)
   testCovarPop()
+  testCovarPop(true)
   testCovarSamp()
+  testCovarSamp(true)
   testCorr()
+  testCorr(true)
 }
diff --git a/external/docker-integration-tests/src/test/scala/org/apache/spark/sql/jdbc/v2/V2JDBCTest.scala b/external/docker-integration-tests/src/test/scala/org/apache/spark/sql/jdbc/v2/V2JDBCTest.scala
index 6ea2099346781..ebd5b844cbc9b 100644
--- a/external/docker-integration-tests/src/test/scala/org/apache/spark/sql/jdbc/v2/V2JDBCTest.scala
+++ b/external/docker-integration-tests/src/test/scala/org/apache/spark/sql/jdbc/v2/V2JDBCTest.scala
@@ -386,10 +386,11 @@ private[v2] trait V2JDBCTest extends SharedSparkSession with DockerIntegrationFu
 
   protected def caseConvert(tableName: String): String = tableName
 
-  protected def testVarPop(): Unit = {
-    test(s"scan with aggregate push-down: VAR_POP") {
-      val df = sql(s"SELECT VAR_POP(bonus) FROM $catalogAndNamespace.${caseConvert("employee")}" +
-        " WHERE dept > 0 GROUP BY dept ORDER BY dept")
+  protected def testVarPop(isDistinct: Boolean = false): Unit = {
+    val distinct = if (isDistinct) "DISTINCT " else ""
+    test(s"scan with aggregate push-down: VAR_POP with distinct: $isDistinct") {
+      val df = sql(s"SELECT VAR_POP(${distinct}bonus) FROM $catalogAndNamespace." +
+        s"${caseConvert("employee")} WHERE dept > 0 GROUP BY dept ORDER BY dept")
       checkFilterPushed(df)
       checkAggregateRemoved(df)
       checkAggregatePushed(df, "VAR_POP")
@@ -401,11 +402,12 @@ private[v2] trait V2JDBCTest extends SharedSparkSession with DockerIntegrationFu
     }
   }
 
-  protected def testVarSamp(): Unit = {
-    test(s"scan with aggregate push-down: VAR_SAMP") {
+  protected def testVarSamp(isDistinct: Boolean = false): Unit = {
+    val distinct = if (isDistinct) "DISTINCT " else ""
+    test(s"scan with aggregate push-down: VAR_SAMP with distinct: $isDistinct") {
       val df = sql(
-        s"SELECT VAR_SAMP(bonus) FROM $catalogAndNamespace.${caseConvert("employee")}" +
-        " WHERE dept > 0 GROUP BY dept ORDER BY dept")
+        s"SELECT VAR_SAMP(${distinct}bonus) FROM $catalogAndNamespace." +
+        s"${caseConvert("employee")} WHERE dept > 0 GROUP BY dept ORDER BY dept")
       checkFilterPushed(df)
       checkAggregateRemoved(df)
       checkAggregatePushed(df, "VAR_SAMP")
@@ -417,11 +419,12 @@ private[v2] trait V2JDBCTest extends SharedSparkSession with DockerIntegrationFu
     }
   }
 
-  protected def testStddevPop(): Unit = {
-    test("scan with aggregate push-down: STDDEV_POP") {
+  protected def testStddevPop(isDistinct: Boolean = false): Unit = {
+    val distinct = if (isDistinct) "DISTINCT " else ""
+    test(s"scan with aggregate push-down: STDDEV_POP with distinct: $isDistinct") {
       val df = sql(
-        s"SELECT STDDEV_POP(bonus) FROM $catalogAndNamespace.${caseConvert("employee")}" +
-        " WHERE dept > 0 GROUP BY dept ORDER BY dept")
+        s"SELECT STDDEV_POP(${distinct}bonus) FROM $catalogAndNamespace." +
+        s"${caseConvert("employee")} WHERE dept > 0 GROUP BY dept ORDER BY dept")
       checkFilterPushed(df)
       checkAggregateRemoved(df)
       checkAggregatePushed(df, "STDDEV_POP")
@@ -433,11 +436,12 @@ private[v2] trait V2JDBCTest extends SharedSparkSession with DockerIntegrationFu
     }
   }
 
-  protected def testStddevSamp(): Unit = {
-    test("scan with aggregate push-down: STDDEV_SAMP") {
+  protected def testStddevSamp(isDistinct: Boolean = false): Unit = {
+    val distinct = if (isDistinct) "DISTINCT " else ""
+    test(s"scan with aggregate push-down: STDDEV_SAMP with distinct: $isDistinct") {
       val df = sql(
-        s"SELECT STDDEV_SAMP(bonus) FROM $catalogAndNamespace.${caseConvert("employee")}" +
-        " WHERE dept > 0 GROUP BY dept ORDER BY dept")
+        s"SELECT STDDEV_SAMP(${distinct}bonus) FROM $catalogAndNamespace." +
+        s"${caseConvert("employee")} WHERE dept > 0 GROUP BY dept ORDER BY dept")
       checkFilterPushed(df)
       checkAggregateRemoved(df)
       checkAggregatePushed(df, "STDDEV_SAMP")
@@ -449,11 +453,12 @@ private[v2] trait V2JDBCTest extends SharedSparkSession with DockerIntegrationFu
     }
   }
 
-  protected def testCovarPop(): Unit = {
-    test("scan with aggregate push-down: COVAR_POP") {
+  protected def testCovarPop(isDistinct: Boolean = false): Unit = {
+    val distinct = if (isDistinct) "DISTINCT " else ""
+    test(s"scan with aggregate push-down: COVAR_POP with distinct: $isDistinct") {
       val df = sql(
-        s"SELECT COVAR_POP(bonus, bonus) FROM $catalogAndNamespace.${caseConvert("employee")}" +
-        " WHERE dept > 0 GROUP BY dept ORDER BY dept")
+        s"SELECT COVAR_POP(${distinct}bonus, bonus) FROM $catalogAndNamespace." +
+        s"${caseConvert("employee")} WHERE dept > 0 GROUP BY dept ORDER BY dept")
       checkFilterPushed(df)
       checkAggregateRemoved(df)
       checkAggregatePushed(df, "COVAR_POP")
@@ -465,11 +470,12 @@ private[v2] trait V2JDBCTest extends SharedSparkSession with DockerIntegrationFu
     }
   }
 
-  protected def testCovarSamp(): Unit = {
-    test("scan with aggregate push-down: COVAR_SAMP") {
+  protected def testCovarSamp(isDistinct: Boolean = false): Unit = {
+    val distinct = if (isDistinct) "DISTINCT " else ""
+    test(s"scan with aggregate push-down: COVAR_SAMP with distinct: $isDistinct") {
       val df = sql(
-        s"SELECT COVAR_SAMP(bonus, bonus) FROM $catalogAndNamespace.${caseConvert("employee")}" +
-        " WHERE dept > 0 GROUP BY dept ORDER BY dept")
+        s"SELECT COVAR_SAMP(${distinct}bonus, bonus) FROM $catalogAndNamespace." +
+        s"${caseConvert("employee")} WHERE dept > 0 GROUP BY dept ORDER BY dept")
       checkFilterPushed(df)
       checkAggregateRemoved(df)
       checkAggregatePushed(df, "COVAR_SAMP")
@@ -481,11 +487,12 @@ private[v2] trait V2JDBCTest extends SharedSparkSession with DockerIntegrationFu
     }
   }
 
-  protected def testCorr(): Unit = {
-    test("scan with aggregate push-down: CORR") {
+  protected def testCorr(isDistinct: Boolean = false): Unit = {
+    val distinct = if (isDistinct) "DISTINCT " else ""
+    test(s"scan with aggregate push-down: CORR with distinct: $isDistinct") {
       val df = sql(
-        s"SELECT CORR(bonus, bonus) FROM $catalogAndNamespace.${caseConvert("employee")}" +
-        " WHERE dept > 0 GROUP BY dept ORDER BY dept")
+        s"SELECT CORR(${distinct}bonus, bonus) FROM $catalogAndNamespace." +
+        s"${caseConvert("employee")} WHERE dept > 0 GROUP BY dept ORDER BY dept")
       checkFilterPushed(df)
       checkAggregateRemoved(df)
       checkAggregatePushed(df, "CORR")
diff --git a/sql/core/src/main/scala/org/apache/spark/sql/jdbc/DB2Dialect.scala b/sql/core/src/main/scala/org/apache/spark/sql/jdbc/DB2Dialect.scala
index baa772f4546a4..6af5cc00ef5db 100644
--- a/sql/core/src/main/scala/org/apache/spark/sql/jdbc/DB2Dialect.scala
+++ b/sql/core/src/main/scala/org/apache/spark/sql/jdbc/DB2Dialect.scala
@@ -30,6 +30,7 @@ private object DB2Dialect extends JdbcDialect {
   override def canHandle(url: String): Boolean =
     url.toLowerCase(Locale.ROOT).startsWith("jdbc:db2")
 
+  // See https://www.ibm.com/docs/en/db2/11.5?topic=functions-aggregate
   override def compileAggregate(aggFunction: AggregateFunc): Option[String] = {
     super.compileAggregate(aggFunction).orElse(
       aggFunction match {
@@ -37,6 +38,24 @@ private object DB2Dialect extends JdbcDialect {
           assert(f.inputs().length == 1)
           val distinct = if (f.isDistinct) "DISTINCT " else ""
           Some(s"VARIANCE($distinct${f.inputs().head})")
+        case f: GeneralAggregateFunc if f.name() == "VAR_SAMP" =>
+          assert(f.inputs().length == 1)
+          val distinct = if (f.isDistinct) "DISTINCT " else ""
+          Some(s"VARIANCE_SAMP($distinct${f.inputs().head})")
+        case f: GeneralAggregateFunc if f.name() == "STDDEV_POP" =>
+          assert(f.inputs().length == 1)
+          val distinct = if (f.isDistinct) "DISTINCT " else ""
+          Some(s"STDDEV($distinct${f.inputs().head})")
+        case f: GeneralAggregateFunc if f.name() == "STDDEV_SAMP" =>
+          assert(f.inputs().length == 1)
+          val distinct = if (f.isDistinct) "DISTINCT " else ""
+          Some(s"STDDEV_SAMP($distinct${f.inputs().head})")
+        case f: GeneralAggregateFunc if f.name() == "COVAR_POP" && f.isDistinct == false =>
+          assert(f.inputs().length == 2)
+          Some(s"COVARIANCE(${f.inputs().head}, ${f.inputs().last})")
+        case f: GeneralAggregateFunc if f.name() == "COVAR_SAMP" && f.isDistinct == false =>
+          assert(f.inputs().length == 2)
+          Some(s"COVARIANCE_SAMP(${f.inputs().head}, ${f.inputs().last})")
         case _ => None
       }
     )
diff --git a/sql/core/src/main/scala/org/apache/spark/sql/jdbc/DerbyDialect.scala b/sql/core/src/main/scala/org/apache/spark/sql/jdbc/DerbyDialect.scala
index e87d4d08ae031..bf838b8ed66eb 100644
--- a/sql/core/src/main/scala/org/apache/spark/sql/jdbc/DerbyDialect.scala
+++ b/sql/core/src/main/scala/org/apache/spark/sql/jdbc/DerbyDialect.scala
@@ -30,25 +30,22 @@ private object DerbyDialect extends JdbcDialect {
   override def canHandle(url: String): Boolean =
     url.toLowerCase(Locale.ROOT).startsWith("jdbc:derby")
 
+  // See https://db.apache.org/derby/docs/10.15/ref/index.html
   override def compileAggregate(aggFunction: AggregateFunc): Option[String] = {
     super.compileAggregate(aggFunction).orElse(
       aggFunction match {
-        case f: GeneralAggregateFunc if f.name() == "VAR_POP" =>
+        case f: GeneralAggregateFunc if f.name() == "VAR_POP" && f.isDistinct == false =>
           assert(f.inputs().length == 1)
-          val distinct = if (f.isDistinct) "DISTINCT " else ""
-          Some(s"VAR_POP($distinct${f.inputs().head})")
-        case f: GeneralAggregateFunc if f.name() == "VAR_SAMP" =>
+          Some(s"VAR_POP(${f.inputs().head})")
+        case f: GeneralAggregateFunc if f.name() == "VAR_SAMP" && f.isDistinct == false =>
           assert(f.inputs().length == 1)
-          val distinct = if (f.isDistinct) "DISTINCT " else ""
-          Some(s"VAR_SAMP($distinct${f.inputs().head})")
-        case f: GeneralAggregateFunc if f.name() == "STDDEV_POP" =>
+          Some(s"VAR_SAMP(${f.inputs().head})")
+        case f: GeneralAggregateFunc if f.name() == "STDDEV_POP" && f.isDistinct == false =>
           assert(f.inputs().length == 1)
-          val distinct = if (f.isDistinct) "DISTINCT " else ""
-          Some(s"STDDEV_POP($distinct${f.inputs().head})")
-        case f: GeneralAggregateFunc if f.name() == "STDDEV_SAMP" =>
+          Some(s"STDDEV_POP(${f.inputs().head})")
+        case f: GeneralAggregateFunc if f.name() == "STDDEV_SAMP" && f.isDistinct == false =>
           assert(f.inputs().length == 1)
-          val distinct = if (f.isDistinct) "DISTINCT " else ""
-          Some(s"STDDEV_SAMP($distinct${f.inputs().head})")
+          Some(s"STDDEV_SAMP(${f.inputs().head})")
         case _ => None
       }
     )
@@ -72,7 +69,7 @@ private object DerbyDialect extends JdbcDialect {
 
   override def isCascadingTruncateTable(): Option[Boolean] = Some(false)
 
-  // See https://db.apache.org/derby/docs/10.5/ref/rrefsqljrenametablestatement.html
+  // See https://db.apache.org/derby/docs/10.15/ref/rrefsqljrenametablestatement.html
   override def renameTable(oldTable: String, newTable: String): String = {
     s"RENAME TABLE $oldTable TO $newTable"
   }
diff --git a/sql/core/src/main/scala/org/apache/spark/sql/jdbc/MsSqlServerDialect.scala b/sql/core/src/main/scala/org/apache/spark/sql/jdbc/MsSqlServerDialect.scala
index 3d8a48a66ea8f..841f1c87319b5 100644
--- a/sql/core/src/main/scala/org/apache/spark/sql/jdbc/MsSqlServerDialect.scala
+++ b/sql/core/src/main/scala/org/apache/spark/sql/jdbc/MsSqlServerDialect.scala
@@ -40,6 +40,9 @@ private object MsSqlServerDialect extends JdbcDialect {
   override def canHandle(url: String): Boolean =
     url.toLowerCase(Locale.ROOT).startsWith("jdbc:sqlserver")
 
+  // scalastyle:off line.size.limit
+  // See https://docs.microsoft.com/en-us/sql/t-sql/functions/aggregate-functions-transact-sql?view=sql-server-ver15
+  // scalastyle:on line.size.limit
   override def compileAggregate(aggFunction: AggregateFunc): Option[String] = {
     super.compileAggregate(aggFunction).orElse(
       aggFunction match {
diff --git a/sql/core/src/main/scala/org/apache/spark/sql/jdbc/MySQLDialect.scala b/sql/core/src/main/scala/org/apache/spark/sql/jdbc/MySQLDialect.scala
index 3cca81048e812..d73721de962d7 100644
--- a/sql/core/src/main/scala/org/apache/spark/sql/jdbc/MySQLDialect.scala
+++ b/sql/core/src/main/scala/org/apache/spark/sql/jdbc/MySQLDialect.scala
@@ -38,25 +38,22 @@ private case object MySQLDialect extends JdbcDialect with SQLConfHelper {
   override def canHandle(url : String): Boolean =
     url.toLowerCase(Locale.ROOT).startsWith("jdbc:mysql")
 
+  // See https://dev.mysql.com/doc/refman/8.0/en/aggregate-functions.html
   override def compileAggregate(aggFunction: AggregateFunc): Option[String] = {
     super.compileAggregate(aggFunction).orElse(
       aggFunction match {
-        case f: GeneralAggregateFunc if f.name() == "VAR_POP" =>
+        case f: GeneralAggregateFunc if f.name() == "VAR_POP" && f.isDistinct == false =>
           assert(f.inputs().length == 1)
-          val distinct = if (f.isDistinct) "DISTINCT " else ""
-          Some(s"VAR_POP($distinct${f.inputs().head})")
-        case f: GeneralAggregateFunc if f.name() == "VAR_SAMP" =>
+          Some(s"VAR_POP(${f.inputs().head})")
+        case f: GeneralAggregateFunc if f.name() == "VAR_SAMP" && f.isDistinct == false =>
           assert(f.inputs().length == 1)
-          val distinct = if (f.isDistinct) "DISTINCT " else ""
-          Some(s"VAR_SAMP($distinct${f.inputs().head})")
-        case f: GeneralAggregateFunc if f.name() == "STDDEV_POP" =>
+          Some(s"VAR_SAMP(${f.inputs().head})")
+        case f: GeneralAggregateFunc if f.name() == "STDDEV_POP" && f.isDistinct == false =>
           assert(f.inputs().length == 1)
-          val distinct = if (f.isDistinct) "DISTINCT " else ""
-          Some(s"STDDEV_POP($distinct${f.inputs().head})")
-        case f: GeneralAggregateFunc if f.name() == "STDDEV_SAMP" =>
+          Some(s"STDDEV_POP(${f.inputs().head})")
+        case f: GeneralAggregateFunc if f.name() == "STDDEV_SAMP" && f.isDistinct == false =>
           assert(f.inputs().length == 1)
-          val distinct = if (f.isDistinct) "DISTINCT " else ""
-          Some(s"STDDEV_SAMP($distinct${f.inputs().head})")
+          Some(s"STDDEV_SAMP(${f.inputs().head})")
         case _ => None
       }
     )
diff --git a/sql/core/src/main/scala/org/apache/spark/sql/jdbc/OracleDialect.scala b/sql/core/src/main/scala/org/apache/spark/sql/jdbc/OracleDialect.scala
index 4fe7d93142c1e..71db7e9285f5e 100644
--- a/sql/core/src/main/scala/org/apache/spark/sql/jdbc/OracleDialect.scala
+++ b/sql/core/src/main/scala/org/apache/spark/sql/jdbc/OracleDialect.scala
@@ -34,37 +34,33 @@ private case object OracleDialect extends JdbcDialect {
   override def canHandle(url: String): Boolean =
     url.toLowerCase(Locale.ROOT).startsWith("jdbc:oracle")
 
+  // scalastyle:off line.size.limit
+  // https://docs.oracle.com/en/database/oracle/oracle-database/19/sqlrf/Aggregate-Functions.html#GUID-62BE676B-AF18-4E63-BD14-25206FEA0848
+  // scalastyle:on line.size.limit
   override def compileAggregate(aggFunction: AggregateFunc): Option[String] = {
     super.compileAggregate(aggFunction).orElse(
       aggFunction match {
-        case f: GeneralAggregateFunc if f.name() == "VAR_POP" =>
+        case f: GeneralAggregateFunc if f.name() == "VAR_POP" && f.isDistinct == false =>
           assert(f.inputs().length == 1)
-          val distinct = if (f.isDistinct) "DISTINCT " else ""
-          Some(s"VAR_POP($distinct${f.inputs().head})")
-        case f: GeneralAggregateFunc if f.name() == "VAR_SAMP" =>
+          Some(s"VAR_POP(${f.inputs().head})")
+        case f: GeneralAggregateFunc if f.name() == "VAR_SAMP" && f.isDistinct == false =>
           assert(f.inputs().length == 1)
-          val distinct = if (f.isDistinct) "DISTINCT " else ""
-          Some(s"VAR_SAMP($distinct${f.inputs().head})")
-        case f: GeneralAggregateFunc if f.name() == "STDDEV_POP" =>
+          Some(s"VAR_SAMP(${f.inputs().head})")
+        case f: GeneralAggregateFunc if f.name() == "STDDEV_POP" && f.isDistinct == false =>
           assert(f.inputs().length == 1)
-          val distinct = if (f.isDistinct) "DISTINCT " else ""
-          Some(s"STDDEV_POP($distinct${f.inputs().head})")
-        case f: GeneralAggregateFunc if f.name() == "STDDEV_SAMP" =>
+          Some(s"STDDEV_POP(${f.inputs().head})")
+        case f: GeneralAggregateFunc if f.name() == "STDDEV_SAMP" && f.isDistinct == false =>
           assert(f.inputs().length == 1)
-          val distinct = if (f.isDistinct) "DISTINCT " else ""
-          Some(s"STDDEV_SAMP($distinct${f.inputs().head})")
-        case f: GeneralAggregateFunc if f.name() == "COVAR_POP" =>
+          Some(s"STDDEV_SAMP(${f.inputs().head})")
+        case f: GeneralAggregateFunc if f.name() == "COVAR_POP" && f.isDistinct == false =>
           assert(f.inputs().length == 2)
-          val distinct = if (f.isDistinct) "DISTINCT " else ""
-          Some(s"COVAR_POP($distinct${f.inputs().head}, ${f.inputs().last})")
-        case f: GeneralAggregateFunc if f.name() == "COVAR_SAMP" =>
+          Some(s"COVAR_POP(${f.inputs().head}, ${f.inputs().last})")
+        case f: GeneralAggregateFunc if f.name() == "COVAR_SAMP" && f.isDistinct == false =>
           assert(f.inputs().length == 2)
-          val distinct = if (f.isDistinct) "DISTINCT " else ""
-          Some(s"COVAR_SAMP($distinct${f.inputs().head}, ${f.inputs().last})")
-        case f: GeneralAggregateFunc if f.name() == "CORR" =>
+          Some(s"COVAR_SAMP(${f.inputs().head}, ${f.inputs().last})")
+        case f: GeneralAggregateFunc if f.name() == "CORR" && f.isDistinct == false =>
           assert(f.inputs().length == 2)
-          val distinct = if (f.isDistinct) "DISTINCT " else ""
-          Some(s"CORR($distinct${f.inputs().head}, ${f.inputs().last})")
+          Some(s"CORR(${f.inputs().head}, ${f.inputs().last})")
         case _ => None
       }
     )
diff --git a/sql/core/src/main/scala/org/apache/spark/sql/jdbc/PostgresDialect.scala b/sql/core/src/main/scala/org/apache/spark/sql/jdbc/PostgresDialect.scala
index 46e79404f3e54..e2023d110ae4b 100644
--- a/sql/core/src/main/scala/org/apache/spark/sql/jdbc/PostgresDialect.scala
+++ b/sql/core/src/main/scala/org/apache/spark/sql/jdbc/PostgresDialect.scala
@@ -36,6 +36,7 @@ private object PostgresDialect extends JdbcDialect with SQLConfHelper {
   override def canHandle(url: String): Boolean =
     url.toLowerCase(Locale.ROOT).startsWith("jdbc:postgresql")
 
+  // See https://www.postgresql.org/docs/8.4/functions-aggregate.html
   override def compileAggregate(aggFunction: AggregateFunc): Option[String] = {
     super.compileAggregate(aggFunction).orElse(
       aggFunction match {
diff --git a/sql/core/src/main/scala/org/apache/spark/sql/jdbc/TeradataDialect.scala b/sql/core/src/main/scala/org/apache/spark/sql/jdbc/TeradataDialect.scala
index 6344667b3180e..13e16d24d048d 100644
--- a/sql/core/src/main/scala/org/apache/spark/sql/jdbc/TeradataDialect.scala
+++ b/sql/core/src/main/scala/org/apache/spark/sql/jdbc/TeradataDialect.scala
@@ -28,6 +28,9 @@ private case object TeradataDialect extends JdbcDialect {
   override def canHandle(url: String): Boolean =
     url.toLowerCase(Locale.ROOT).startsWith("jdbc:teradata")
 
+  // scalastyle:off line.size.limit
+  // See https://docs.teradata.com/r/Teradata-VantageTM-SQL-Functions-Expressions-and-Predicates/March-2019/Aggregate-Functions
+  // scalastyle:on line.size.limit
   override def compileAggregate(aggFunction: AggregateFunc): Option[String] = {
     super.compileAggregate(aggFunction).orElse(
       aggFunction match {
@@ -47,18 +50,15 @@ private case object TeradataDialect extends JdbcDialect {
           assert(f.inputs().length == 1)
           val distinct = if (f.isDistinct) "DISTINCT " else ""
           Some(s"STDDEV_SAMP($distinct${f.inputs().head})")
-        case f: GeneralAggregateFunc if f.name() == "COVAR_POP" =>
+        case f: GeneralAggregateFunc if f.name() == "COVAR_POP" && f.isDistinct == false =>
           assert(f.inputs().length == 2)
-          val distinct = if (f.isDistinct) "DISTINCT " else ""
-          Some(s"COVAR_POP($distinct${f.inputs().head}, ${f.inputs().last})")
-        case f: GeneralAggregateFunc if f.name() == "COVAR_SAMP" =>
+          Some(s"COVAR_POP(${f.inputs().head}, ${f.inputs().last})")
+        case f: GeneralAggregateFunc if f.name() == "COVAR_SAMP" && f.isDistinct == false =>
           assert(f.inputs().length == 2)
-          val distinct = if (f.isDistinct) "DISTINCT " else ""
-          Some(s"COVAR_SAMP($distinct${f.inputs().head}, ${f.inputs().last})")
-        case f: GeneralAggregateFunc if f.name() == "CORR" =>
+          Some(s"COVAR_SAMP(${f.inputs().head}, ${f.inputs().last})")
+        case f: GeneralAggregateFunc if f.name() == "CORR" && f.isDistinct == false =>
           assert(f.inputs().length == 2)
-          val distinct = if (f.isDistinct) "DISTINCT " else ""
-          Some(s"CORR($distinct${f.inputs().head}, ${f.inputs().last})")
+          Some(s"CORR(${f.inputs().head}, ${f.inputs().last})")
         case _ => None
       }
     )