BornhuetterFerguson

BornhuetterFerguson#

class chainladder.BornhuetterFerguson(apriori=1.0, apriori_sigma=0.0, random_state=None)[source]#

The deterministic Bornhuetter Ferguson IBNR model

Parameters:

apriori: float, optional (default=1.0): Multiplier for the sample_weight used in the Bornhuetter Ferguson method. If sample_weight is already an apriori measure of ultimate, then use 1.0. The recommended pratice is to seperate the model parameter assumption and data apart. For example, if the apriori s 80% of premium, it is recommended to set the aprior as 0.8 and leave the premium data in sample_weight argument unmodified.
apriori_sigma: float, optional (default=0.0): Standard deviation of the apriori. When used in conjunction with the bootstrap model, the model samples aprioris from a lognormal distribution using this argument as a standard deviation.
random_state: int, RandomState instance or None, optional (default=None): Seed for sampling from the apriori distribution. This is ignored when using as a deterministic method. If int, random_state is the seed used by the random number generator; If RandomState instance, random_state is the random number generator; If None, the random number generator is the RandomState instance used by np.random.

Attributes:

ultimate_: Triangle: The ultimate losses per the method
ibnr_: Triangle: The IBNR per the method

Examples

Bornhuetter-Ferguson requires an apriori expected ultimate per origin, supplied through sample_weight.

A common idiom for building a flat per-origin apriori is to take any same-shape Triangle, zero it out, and add the desired value. Here is an example.

raa = cl.load_sample("raa")
premium = raa.latest_diagonal * 0 + 40_000  # zero out and add 40,000 to each origin

ibnr = cl.BornhuetterFerguson(apriori=0.7).fit(X=raa, sample_weight=premium).ibnr_
print(ibnr)

              2261
         NaN
  255.707763
  717.772687
 1596.061515
 2658.738155
 5239.441491
 8574.335344
12714.889984
18585.219714
24861.068855

One might be tempted to set never set the aprior and modify the sample_weight directly, and they will result in the same answer, but this is not the recommended practice. It not only add confusion, but it alos mixes the model parameter assumption and data together.

raa = cl.load_sample("raa")
premium = raa.latest_diagonal * 0 + 40_000 * 0.7  # premium is modified by 70%

ibnr = cl.BornhuetterFerguson().fit(X=raa, sample_weight=premium).ibnr_
print(ibnr)

              2261
         NaN
  255.707763
  717.772687
 1596.061515
 2658.738155
 5239.441491
 8574.335344
12714.889984
18585.219714
24861.068855

fit(X, y=None, sample_weight=None)[source]#

Applies the Bornhuetter-Ferguson technique to triangle X

Parameters:

XTriangle: Loss data to which the model will be applied.
yNone: Ignored
sample_weightTriangle: Required exposure to be used in the calculation.

Returns:

selfobject: Returns the instance itself.

Examples

Fit returns the estimator itself, with ultimate_ populated.

tr = cl.load_sample('ukmotor')
apriori = cl.Chainladder().fit(tr).ultimate_ * 0 + 14000
print(cl.BornhuetterFerguson(apriori=1.0).fit(tr, sample_weight=apriori))

BornhuetterFerguson()

predict(X, sample_weight=None)[source]#

Predicts the Bornhuetter-Ferguson ultimate on a new triangle X

Parameters:

XTriangle: Loss data to which the model will be applied.
sample_weightTriangle: Required exposure to be used in the calculation.

Returns:

X_new: Triangle: Loss data with Bornhuetter-Ferguson ultimate applied

Examples

Fit on a prior-period view of the data, then apply the model to the current Triangle and a refreshed apriori.

tr = cl.load_sample('ukmotor')
tr_prior = tr[tr.valuation < tr.valuation_date]
apriori_prior = cl.Chainladder().fit(tr_prior).ultimate_ * 0 + 14000
apriori = cl.Chainladder().fit(tr).ultimate_ * 0 + 14000
model = cl.BornhuetterFerguson(apriori=1.0).fit(
    tr_prior, sample_weight=apriori_prior
)

print(model.predict(tr, sample_weight=apriori).ultimate_)

Inherited Methods

`BornhuetterFerguson.fit_predict`
`BornhuetterFerguson.get_metadata_routing`	Get metadata routing of this object.
`BornhuetterFerguson.get_params`	Get parameters for this estimator.
`BornhuetterFerguson.intersection`	Given two Triangles with mismatched indices, this method aligns their indices
`BornhuetterFerguson.pipe`
`BornhuetterFerguson.set_backend`	Converts triangle array_backend.
`BornhuetterFerguson.set_params`	Set the parameters of this estimator.
`BornhuetterFerguson.to_json`	Serializes triangle object to json format
`BornhuetterFerguson.to_pickle`	Serializes triangle object to pickle.
`BornhuetterFerguson.validate_X`
`BornhuetterFerguson.validate_weight`

BornhuetterFerguson

Contents

BornhuetterFerguson#