xudong963 commented on code in PR #15296:
URL: https://github.com/apache/datafusion/pull/15296#discussion_r2002959262


##########
datafusion/expr-common/src/statistics.rs:
##########
@@ -203,6 +203,121 @@ impl Distribution {
         };
         Ok(dt)
     }
+
+    /// Merges two distributions into a single distribution that represents 
their combined statistics.
+    /// This creates a more general distribution that approximates the mixture 
of the input distributions.
+    pub fn merge(&self, other: &Self) -> Result<Self> {
+        let range_a = self.range()?;
+        let range_b = other.range()?;
+
+        // Determine data type and create combined range
+        let combined_range = range_a.union(&range_b)?;
+
+        // Calculate weights for the mixture distribution
+        let (weight_a, weight_b) = match (range_a.cardinality(), 
range_b.cardinality()) {
+            (Some(ca), Some(cb)) => {
+                let total = (ca + cb) as f64;
+                ((ca as f64) / total, (cb as f64) / total)
+            }
+            _ => (0.5, 0.5), // Equal weights if cardinalities not available
+        };
+
+        // Get the original statistics
+        let mean_a = self.mean()?;
+        let mean_b = other.mean()?;
+        let median_a = self.median()?;
+        let median_b = other.median()?;
+        let var_a = self.variance()?;
+        let var_b = other.variance()?;
+
+        // Always use Float64 for intermediate calculations to avoid truncation
+        // I assume that the target type is always numeric
+        // Todo: maybe we can keep all `ScalarValue` as `Float64` in 
`Distribution`?
+        let calc_type = DataType::Float64;
+
+        // Create weight scalars using Float64 to avoid truncation
+        let weight_a_scalar = ScalarValue::from(weight_a);
+        let weight_b_scalar = ScalarValue::from(weight_b);
+
+        // Calculate combined mean
+        let combined_mean = if mean_a.is_null() || mean_b.is_null() {
+            if mean_a.is_null() {
+                mean_b.clone()
+            } else {
+                mean_a.clone()
+            }
+        } else {
+            // Cast to Float64 for calculation
+            let mean_a_f64 = mean_a.cast_to(&calc_type)?;
+            let mean_b_f64 = mean_b.cast_to(&calc_type)?;
+
+            // Calculate weighted mean
+            mean_a_f64
+                .mul_checked(&weight_a_scalar)?
+                .add_checked(&mean_b_f64.mul_checked(&weight_b_scalar)?)?
+        };
+
+        // Calculate combined median
+        let combined_median = if median_a.is_null() || median_b.is_null() {
+            if median_a.is_null() {
+                median_b
+            } else {
+                median_a
+            }
+        } else {
+            // Cast to Float64 for calculation
+            let median_a_f64 = median_a.cast_to(&calc_type)?;
+            let median_b_f64 = median_b.cast_to(&calc_type)?;
+
+            // Calculate weighted median
+            median_a_f64
+                .mul_checked(&weight_a_scalar)?
+                .add_checked(&median_b_f64.mul_checked(&weight_b_scalar)?)?

Review Comment:
   I add some notes for the method: 
https://github.com/apache/datafusion/pull/15296/commits/5b98f4c5efe5404a6ae4c8609a3574cccc91e9ab



##########
datafusion/expr-common/src/statistics.rs:
##########
@@ -857,6 +857,143 @@ pub fn compute_variance(
     ScalarValue::try_from(target_type)
 }
 
+/// Merges two distributions into a single distribution that represents their 
combined statistics.
+/// This creates a more general distribution that approximates the mixture of 
the input distributions.

Review Comment:
   I added some notes for the method: 
https://github.com/apache/datafusion/pull/15296/commits/5b98f4c5efe5404a6ae4c8609a3574cccc91e9ab



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