diff --git a/tests/statistical/test_generate.py b/tests/statistical/test_generate.py
new file mode 100644
index 00000000..a913274c
--- /dev/null
+++ b/tests/statistical/test_generate.py
@@ -0,0 +1,80 @@
+# Not convinced by name of file
+import numpy as np
+from typing import List, Optional
+from outlines_core.fsm.guide import RegexGuide
+
+def test_generate_length():
+    class MockTokenizer:
+        vocabulary = {"0": 1, "1": 2, "eos": 3}
+        inverse_vocabulary = {1: "0", 2: "1", 3: ""}
+        special_tokens = {"eos"}
+        eos_token_id = 3
+        
+        def length(self):
+            return len(self.vocabulary)
+
+        def convert_token_to_string(self, token):
+            return self.inverse_vocabulary[token]
+    
+    class NextToken:
+        probs: dict[int, List[float]] = {
+            1: [0.3, 0.4, 0.0],
+            2: [0.4, 0.3, 0.1],
+            3: [0, 0, 0]
+        }
+        p0: List[float] = [0.2, 0.8, 0.0]
+        states: List[int] = [1, 2, 3]
+        
+        def __call__(self, token: Optional[int], *, mask: List[int]) -> int:
+            if token is None:
+                prob = [p * m for (p, m) in zip(self.p0, mask)]
+            elif token in self.states:
+                prob = [p * m for (p, m) in zip(self.probs[token], mask)]
+            else:
+                raise ValueError("Should not be reached")
+            return np.random.sample(self.states, p = prob)
+        
+    def generate(model, tokenizer, regex_str) -> str:
+        out_str: str = ""
+        n_tokens = tokenizer.length()
+        
+        fsm = RegexGuide.from_regex(regex_str, tokenizer)
+        
+        state = 0
+        token = None
+        while not fsm.is_final_state(state):
+            allowed = fsm.get_next_instruction(state)
+            mask = [1 if s in allowed else 0 for s in range(1, n_tokens + 1)]
+            token = model(token, mask = mask)
+            out_str += tokenizer.inverse_vocabulary[token]
+            state = fsm.get_next_state(state, token)
+        return out_str
+    
+    n_samples: int = 1000
+    regex_str: str = r"11[01]+|0[01]*"
+    tokenizer = MockTokenizer()
+    model = NextToken()
+    
+    tot = 0
+    for i in range(n_samples):
+        out = generate(model, tokenizer, regex_str)
+        tot += len(out)
+        
+    mean = tot / n_samples
+    print(mean)
+        
+        
+        
+if __name__ == "__main__":
+    test_generate_length()
+        
+        
+        
+        
+        
+        
+    
+            
+            
+            
+    
\ No newline at end of file