Barnett Zehnwirth documentation and formulation rework

chainladder/development/tests/test_barnzehn.py

@@ -40,10 +40,10 @@ def test_bz_2008():
     exposure=np.array([[2.2], [2.4], [2.2], [2.0], [1.9], [1.6], [1.6], [1.8], [2.2], [2.5], [2.6]])
     abc_adj = abc/exposure
 
-    origin_buckets = [(0,1),(2,2),(3,4),(5,10)]
-    dev_buckets = [(24,36),(36,48),(48,84),(84,108),(108,144)]
-    val_buckets = [(1,8),(8,9),(9,12)]
-    
+    origin_buckets = [0,2,3,5]
+    dev_buckets = [12,24,36,72,96,132]
+    val_buckets = [0,7,8,11]
+
     abc_formula = PTF_formula(abc_adj,alpha=origin_buckets,gamma=dev_buckets,iota=val_buckets)
 
     model=cl.BarnettZehnwirth(formula=abc_formula, drop=('1982',72)).fit(abc_adj)

chainladder/utils/utility_functions.py

@@ -772,24 +772,26 @@ def model_diagnostics(model, name=None, groupby=None):
 def PTF_formula(tri: Triangle, alpha: ArrayLike = None, gamma: ArrayLike = None, iota: ArrayLike = None):
     """ Helper formula that builds a patsy formula string for the BarnettZehnwirth 
     estimator.  Each axis's parameters can be grouped together. Groups of origin 
-    parameters (alpha) are set equal, and are specified by a ranges (inclusive). 
+    parameters (alpha) are set equal, and are specified by the first period in each bin. 
     Groups of development (gamma) and valuation (iota) parameters are fit to 
-    separate linear trends, specified as tuples denoting ranges with shared endpoints.
+    separate linear trends, specified a list denoting the endpoints of the linear pieces.
     In other words, development and valuation trends are fit to a piecewise linear model.
     A triangle must be supplied to provide some critical information.
     """
     formula_parts=[]
     if(alpha):
         # The intercept term takes the place of the first alpha
         for ind,a in enumerate(alpha):
-            if(a[0]==0):
+            if(a==0):
                 alpha=alpha[:ind]+alpha[(ind+1):]
-        formula_parts += ['+'.join([f'I({x[0]} <= origin)' for x in alpha])]
-    if(gamma):
+        formula_parts += ['+'.join([f'I({x} <= origin)' for x in alpha])]
+    if(gamma): 
         dgrain = min(tri.development)
-        formula_parts += ['+'.join([f'I((np.minimum({x[1]-dgrain},development) - np.minimum({x[0]-dgrain},development))/{dgrain})' for x in gamma])]
+        for ind in range(1,len(gamma)):
+            formula_parts += ['+'.join([f'I((np.minimum({gamma[ind]},development) - np.minimum({gamma[ind-1]},development))/{dgrain})'])]
     if(iota):
-        formula_parts += ['+'.join([f'I(np.minimum({x[1]-1},valuation) - np.minimum({x[0]-1},valuation))' for x in iota])]
+        for ind in range(1,len(iota)):
+            formula_parts += ['+'.join([f'I(np.minimum({iota[ind]},valuation) - np.minimum({iota[ind-1]},valuation))'])]
     if(formula_parts):
         return '+'.join(formula_parts)
     return ''

docs/library/references.bib

@@ -87,3 +87,11 @@ @article{shapland2016
 	year = {2016},
 	url = {https://live-casact.pantheonsite.io/sites/default/files/2021-02/04-shapland.pdf}
 }
+
+@article{barnett2008,
+    author = {Barnett, G. and Zehnwirth, B.},
+	title = {Modeling with the {M}ultivariate {P}robabilistic {T}rend {F}amily},
+	journal = {Casualty Actuarial Society E-Forum},
+	year = {2008},
+	url = {https://www.casact.org/sites/default/files/database/forum_08fforum_3barnett_zehnwirth.pdf}
+}