diff --git a/requirements.txt b/requirements.txt
index f88df538..fe9291d3 100644
--- a/requirements.txt
+++ b/requirements.txt
@@ -2,4 +2,5 @@
 pyyaml>=6.0
 numpy>=1.21.0
 pandas>=1.3.0
+scipy>=1.7.0
 pyotp>=2.6.0
diff --git a/skills/real-time-var-backtesting-kupiec-test/scripts/kupiec_var_backtester.py b/skills/real-time-var-backtesting-kupiec-test/scripts/kupiec_var_backtester.py
index e60e371b..565521c7 100644
--- a/skills/real-time-var-backtesting-kupiec-test/scripts/kupiec_var_backtester.py
+++ b/skills/real-time-var-backtesting-kupiec-test/scripts/kupiec_var_backtester.py
@@ -1,25 +1,62 @@
+"""
+kupiec_var_backtester: Kupiec POF (Proportion of Failures) Likelihood Ratio test
+for VaR model backtesting.
+"""
 from dataclasses import dataclass
-import scipy.stats as st
+import math
+from typing import Optional
+
+try:
+    import scipy.stats as st
+except ImportError:
+    st = None
+
 
 @dataclass
 class KupiecResult:
     p_value: float
     is_rejected: bool
     exceptions: int
+    stat: float = 0.0
+
 
 class KupiecVaRBacktester:
-    def __init__(self, confidence_level: float = 0.99):
+    def __init__(self, confidence_level: float = 0.99, alpha: float = 0.05):
         self.confidence_level = confidence_level
+        self.alpha = alpha
 
     def run_test(self, total_observations: int, exceptions: int) -> KupiecResult:
-        if total_observations == 0:
-            return KupiecResult(1.0, False, 0)
-        p = 1 - self.confidence_level
-        # binomial test
-        try:
-            res = st.binomtest(exceptions, total_observations, p, alternative='two-sided')
-            p_val = res.pvalue
-        except AttributeError:
-            p_val = st.binom_test(exceptions, total_observations, p, alternative='two-sided')
-        is_rejected = p_val < 0.05
-        return KupiecResult(float(p_val), is_rejected, exceptions)
+        if total_observations <= 0:
+            return KupiecResult(1.0, False, 0, 0.0)
+
+        p = 1.0 - self.confidence_level
+
+        if st is not None:
+            try:
+                res = st.binomtest(exceptions, total_observations, p, alternative='two-sided')
+                p_val = float(res.pvalue)
+            except AttributeError:
+                p_val = float(st.binom_test(exceptions, total_observations, p, alternative='two-sided'))
+            is_rejected = p_val < self.alpha
+            return KupiecResult(p_val, is_rejected, exceptions)
+
+        # Pure Python Kupiec POF Likelihood Ratio test fallback
+        x = exceptions
+        N = total_observations
+        if x == 0:
+            lr_stat = -2.0 * (N * math.log(1.0 - p))
+        elif x == N:
+            lr_stat = -2.0 * (N * math.log(p))
+        else:
+            pi_hat = x / N
+            num = ((1.0 - p) ** (N - x)) * (p ** x)
+            den = ((1.0 - pi_hat) ** (N - x)) * (pi_hat ** x)
+            if den > 0 and num > 0:
+                lr_stat = -2.0 * math.log(num / den)
+            else:
+                lr_stat = 0.0
+
+        # Critical value for Chi-Square(1) at alpha=0.05 is 3.841459
+        is_rejected = lr_stat > 3.841459
+        p_val = math.exp(-lr_stat / 2.0)  # Approx p-value under Chi2(1)
+        return KupiecResult(p_val, is_rejected, exceptions, stat=lr_stat)