docs: add tail estimator doctest examples

chainladder/tails/bondy.py

@@ -44,6 +44,29 @@ class TailBondy(TailBase):
     --------
     TailCurve
 
+    Examples
+    --------
+    Start the Bondy fit later when earlier link ratios are too volatile for the
+    selected tail. The fitted exponent changes because fewer ages enter the
+    tail regression.
+
+    .. testsetup::
+
+        import chainladder as cl
+
+    .. testcode::
+
+        dev = cl.Development().fit_transform(cl.load_sample("raa"))
+        b_def = cl.TailBondy().fit(dev)
+        b_12 = cl.TailBondy(earliest_age=12).fit(dev)
+        print(round(float(b_def.b_.iloc[0, 0]), 6))
+        print(round(float(b_12.b_.iloc[0, 0]), 6))
+
+    .. testoutput::
+
+        0.5
+        0.48451
+
     """
 
     def __init__(self, earliest_age=None, attachment_age=None, projection_period=12):

chainladder/tails/clark.py

@@ -45,6 +45,29 @@ class TailClark(TailBase):
     norm_resid_: Triangle
         The "Normalized" Residuals of the model according to Clark.
 
+    Examples
+    --------
+    Compare Clark growth curves when the selected tail shape is part of the
+    modeling judgment. The tail LDF changes because each curve extrapolates the
+    remaining development differently.
+
+    .. testsetup::
+
+        import chainladder as cl
+
+    .. testcode::
+
+        dev = cl.Development().fit_transform(cl.load_sample("raa"))
+        log = cl.TailClark(growth="loglogistic").fit(dev)
+        wei = cl.TailClark(growth="weibull").fit(dev)
+        print(round(float(log.ldf_.values[0, 0, 0, -1]), 3))
+        print(round(float(wei.ldf_.values[0, 0, 0, -1]), 3))
+
+    .. testoutput::
+
+        1.189
+        1.014
+
     """
 
     def __init__(self, growth="loglogistic", truncation_age=None,

chainladder/tails/curve.py

@@ -55,6 +55,31 @@ class TailCurve(TailBase):
         Slope parameter of the curve fit.
     intercept : DataFrame
         Intercept parameter of the curve fit.
+
+    Examples
+    --------
+    Compare parametric tail curves when the same development pattern can
+    support multiple extrapolation shapes. The last-period LDF reflects the
+    selected curve family.
+
+    .. testsetup::
+
+        import chainladder as cl
+
+    .. testcode::
+
+        tri = cl.load_sample("tail_sample")
+        dev = cl.Development().fit_transform(tri)
+        exp = cl.TailCurve(curve="exponential", extrap_periods=5).fit(dev)
+        inv = cl.TailCurve(curve="inverse_power", extrap_periods=5).fit(dev)
+        print(round(float(exp.ldf_.values[0, 0, 0, -1]), 6))
+        print(round(float(inv.ldf_.values[0, 0, 0, -1]), 6))
+
+    .. testoutput::
+
+        1.0093
+        1.039271
+
     """
 
     def __init__(