--- a/src/actuarialmath/mortalitylaws.py
+++ b/src/actuarialmath/mortalitylaws.py
@@ -112,7 +112,9 @@
             return ((omega-(x+s+t))/(omega-(x+s)))**alpha
 
         def _f(x: int, s,t : float) -> float:
-            return alpha / (omega - (x+s))
+            remaining = omega - (x+s)
+            return (alpha / remaining
+                    * ((remaining - t) / remaining)**(alpha - 1))
 
         self.set_survival(mu=_mu, l=_l, S=_S, f=_f, minage=0, maxage=omega)
         self.omega_ = omega  # store omega parameter