diff --git a/src/Functions/randDistribution.cpp b/src/Functions/randDistribution.cpp
index dc2ddf2ef24..10a3280010c 100644
--- a/src/Functions/randDistribution.cpp
+++ b/src/Functions/randDistribution.cpp
@@ -1,6 +1,7 @@
 #include <Functions/IFunction.h>
 #include <Functions/FunctionHelpers.h>
 #include <Functions/FunctionFactory.h>
+#include <Core/Field.h>
 #include <Common/Exception.h>
 #include <Common/thread_local_rng.h>
 #include <Common/NaNUtils.h>
@@ -21,7 +22,6 @@ namespace DB
 namespace ErrorCodes
 {
     extern const int ILLEGAL_TYPE_OF_ARGUMENT;
-    extern const int ILLEGAL_COLUMN;
     extern const int BAD_ARGUMENTS;
     extern const int LOGICAL_ERROR;
     extern const int NUMBER_OF_ARGUMENTS_DOESNT_MATCH;
@@ -93,7 +93,7 @@ struct ChiSquaredDistribution
 
     static void generate(Float64 degree_of_freedom, ColumnFloat64::Container & container)
     {
-        if (degree_of_freedom <= 0)
+        if (!container.empty() && degree_of_freedom <= 0)
             throw Exception(ErrorCodes::BAD_ARGUMENTS, "Argument (degrees of freedom) of function {} should be greater than zero", getName());
 
         auto distribution = std::chi_squared_distribution<>(degree_of_freedom);
@@ -110,7 +110,7 @@ struct StudentTDistribution
 
     static void generate(Float64 degree_of_freedom, ColumnFloat64::Container & container)
     {
-        if (degree_of_freedom <= 0)
+        if (!container.empty() && degree_of_freedom <= 0)
             throw Exception(ErrorCodes::BAD_ARGUMENTS, "Argument (degrees of freedom) of function {} should be greater than zero", getName());
 
         auto distribution = std::student_t_distribution<>(degree_of_freedom);
@@ -127,7 +127,7 @@ struct FisherFDistribution
 
     static void generate(Float64 d1, Float64 d2, ColumnFloat64::Container & container)
     {
-        if (d1 <= 0 || d2 <= 0)
+        if (!container.empty() && (d1 <= 0 || d2 <= 0))
             throw Exception(ErrorCodes::BAD_ARGUMENTS, "Argument (degrees of freedom) of function {} should be greater than zero", getName());
 
         auto distribution = std::fisher_f_distribution<>(d1, d2);
@@ -215,9 +215,8 @@ template <typename Distribution>
 class FunctionRandomDistribution : public IFunction
 {
 private:
-
     template <typename ResultType>
-    ResultType getParameterFromConstColumn(size_t parameter_number, const ColumnsWithTypeAndName & arguments) const
+    ResultType getParameterFromColumn(size_t parameter_number, const ColumnsWithTypeAndName & arguments) const
     {
         if (parameter_number >= arguments.size())
             throw Exception(
@@ -226,11 +225,22 @@ private:
                             parameter_number, arguments.size());
 
         const IColumn * col = arguments[parameter_number].column.get();
+        ResultType parameter;
 
-        if (!isColumnConst(*col))
-            throw Exception(ErrorCodes::ILLEGAL_COLUMN, "Parameter number {} of function {} must be constant.", parameter_number, getName());
-
-        auto parameter = applyVisitor(FieldVisitorConvertToNumber<ResultType>(), assert_cast<const ColumnConst &>(*col).getField());
+        if (const ColumnVector<ResultType> * col_in = checkAndGetColumn<ColumnVector<ResultType>>(col))
+        {
+            parameter = *col_in->getData().data();
+        }
+        else if (isColumnConst(*col))
+        {
+            parameter = applyVisitor(FieldVisitorConvertToNumber<ResultType>(), assert_cast<const ColumnConst &>(*col).getField());
+        }
+        else
+        {
+            auto expected_type = Field(Field::Types::Which(Field::TypeToEnum<std::decay_t<ResultType>>::value)).getTypeName();
+            throw Exception(ErrorCodes::BAD_ARGUMENTS, "Parameter number {} of function {} is expected to be {} but is {}",
+                parameter_number, getName(), expected_type, col->getName());
+        }
 
         if (isNaN(parameter) || !std::isfinite(parameter))
             throw Exception(ErrorCodes::BAD_ARGUMENTS, "Parameter number {} of function {} cannot be NaN of infinite", parameter_number, getName());
@@ -278,21 +288,21 @@ public:
         {
             auto res_column = ColumnUInt8::create(input_rows_count);
             auto & res_data = res_column->getData();
-            Distribution::generate(getParameterFromConstColumn<Float64>(0, arguments), res_data);
+            Distribution::generate(getParameterFromColumn<Float64>(0, arguments), res_data);
             return res_column;
         }
         else if constexpr (std::is_same_v<Distribution, BinomialDistribution> || std::is_same_v<Distribution, NegativeBinomialDistribution>)
         {
             auto res_column = ColumnUInt64::create(input_rows_count);
             auto & res_data = res_column->getData();
-            Distribution::generate(getParameterFromConstColumn<UInt64>(0, arguments), getParameterFromConstColumn<Float64>(1, arguments), res_data);
+            Distribution::generate(getParameterFromColumn<UInt64>(0, arguments), getParameterFromColumn<Float64>(1, arguments), res_data);
             return res_column;
         }
         else if constexpr (std::is_same_v<Distribution, PoissonDistribution>)
         {
             auto res_column = ColumnUInt64::create(input_rows_count);
             auto & res_data = res_column->getData();
-            Distribution::generate(getParameterFromConstColumn<UInt64>(0, arguments), res_data);
+            Distribution::generate(getParameterFromColumn<UInt64>(0, arguments), res_data);
             return res_column;
         }
         else
@@ -301,11 +311,11 @@ public:
             auto & res_data = res_column->getData();
             if constexpr (Distribution::getNumberOfArguments() == 1)
             {
-                Distribution::generate(getParameterFromConstColumn<Float64>(0, arguments), res_data);
+                Distribution::generate(getParameterFromColumn<Float64>(0, arguments), res_data);
             }
             else if constexpr (Distribution::getNumberOfArguments() == 2)
             {
-                Distribution::generate(getParameterFromConstColumn<Float64>(0, arguments), getParameterFromConstColumn<Float64>(1, arguments), res_data);
+                Distribution::generate(getParameterFromColumn<Float64>(0, arguments), getParameterFromColumn<Float64>(1, arguments), res_data);
             }
             else
             {
diff --git a/tests/queries/0_stateless/02462_distributions.reference b/tests/queries/0_stateless/02462_distributions.reference
index 56b04bcb856..2341fe20bcc 100644
--- a/tests/queries/0_stateless/02462_distributions.reference
+++ b/tests/queries/0_stateless/02462_distributions.reference
@@ -10,3 +10,5 @@ Ok
 Ok
 Ok
 Ok
+Ok
+Ok
diff --git a/tests/queries/0_stateless/02462_distributions.sql b/tests/queries/0_stateless/02462_distributions.sql
index b45dc897f2a..62a3ec3f6fa 100644
--- a/tests/queries/0_stateless/02462_distributions.sql
+++ b/tests/queries/0_stateless/02462_distributions.sql
@@ -22,3 +22,7 @@ SELECT DISTINCT if (a >= toFloat64(0), 'Ok', 'Fail') FROM (SELECT randNegativeBi
 SELECT DISTINCT if (a >= toFloat64(0), 'Ok', 'Fail') FROM (SELECT randPoisson(44) AS a FROM numbers(100000));
 # No errors
 SELECT randUniform(1, 2, 1), randNormal(0, 1, 'abacaba'), randLogNormal(0, 10, 'b'), randChiSquared(1, 1), randStudentT(7, '8'), randFisherF(23, 42, 100), randBernoulli(0.5, 2), randBinomial(3, 0.5, 1), randNegativeBinomial(3, 0.5, 2), randPoisson(44, 44) FORMAT Null;
+# Values should be >= 0
+SELECT DISTINCT if (a >= toFloat64(-15), 'Ok', 'Fail') FROM (SELECT randNormal(randNormal(0, 1), randUniform(1, 2)) AS a FROM numbers(10000));
+# Values should be >= 0
+SELECT DISTINCT if (a >= toFloat64(0), 'Ok', 'Fail') FROM (SELECT randUniform(randUniform(0, 1), randUniform(1, 2)) AS a FROM numbers(10000));
\ No newline at end of file