From ac5e8ac13f4c8f0edd466a96990403a33b2cdb67 Mon Sep 17 00:00:00 2001
From: ratplier <133662217+ratplier@users.noreply.github.com>
Date: Tue, 25 Nov 2025 16:11:15 -0600
Subject: [PATCH 1/2] improve mean to use kahan summation

---
 src/sampler.luau | 8 +++++++-
 1 file changed, 7 insertions(+), 1 deletion(-)

diff --git a/src/sampler.luau b/src/sampler.luau
index 56d3a03..a0c7b8f 100644
--- a/src/sampler.luau
+++ b/src/sampler.luau
@@ -380,9 +380,15 @@ local function ANALYZE(sample: Sample, options: AnalyzeOptions?): SampleStats
 	-- Calculate MAD (median absolute deviation)
 	local mad = calculate_mad(sample, median)
 
+	-- Calculate mean (Kahan summation)
 	local sum = 0
+	local correction = 0
 	for _, value in sample do
-		sum += value
+		local adjusted_value = value - correction
+		local target = sum + adjusted_value
+
+		correction = (target - sum) - adjusted_value
+		sum = target            
 	end
 	local mean = sum / n
 

From ff8167049f22790051a4bcd09c0d76143f4a30ae Mon Sep 17 00:00:00 2001
From: ratplier <133662217+ratplier@users.noreply.github.com>
Date: Tue, 25 Nov 2025 16:42:57 -0600
Subject: [PATCH 2/2] change kahan to neumaier summation to account for edge
 cases

---
 src/sampler.luau | 14 ++++++++------
 1 file changed, 8 insertions(+), 6 deletions(-)

diff --git a/src/sampler.luau b/src/sampler.luau
index a0c7b8f..d07fbd1 100644
--- a/src/sampler.luau
+++ b/src/sampler.luau
@@ -380,17 +380,19 @@ local function ANALYZE(sample: Sample, options: AnalyzeOptions?): SampleStats
 	-- Calculate MAD (median absolute deviation)
 	local mad = calculate_mad(sample, median)
 
-	-- Calculate mean (Kahan summation)
+	-- Calculate mean (Neumaier summation)
 	local sum = 0
 	local correction = 0
 	for _, value in sample do
-		local adjusted_value = value - correction
-		local target = sum + adjusted_value
+		local target = sum + value
 
-		correction = (target - sum) - adjusted_value
-		sum = target            
+		if math.abs(sum) >= math.abs(value) then
+			correction += (sum - target) + value
+		else
+			correction += (value - target) + sum
+		end
 	end
-	local mean = sum / n
+	local mean = (sum + correction) / n
 
 	-- Calculate variance and standard deviation
 	local variance_sum = 0