BootstrapODPSample

class chainladder.BootstrapODPSample(n_sims=1000, n_periods=-1, hat_adj=True, drop=None, drop_high=None, drop_low=None, drop_valuation=None, random_state=None)

Class to generate bootstrap samples of triangles. Currently this Only supports ‘single’ triangles (single index and single column).

Parameters:

n_sims: int (default=1000)

Number of simulations to generate

n_periods: integer, optional (default=-1)

number of origin periods to be used in the ldf average calculation. For all origin periods, set n_periods=-1

hat_adj: bool (default=False)

Adjust standardized Pearson residuals with the hat matrix adjustment factor. If false, Degree of Freedom adjustment is used.

drop: tuple or list of tuples

Drops specific origin/development combination(s) from residual sample

drop_high: bool or list of bool (default=None)

Drops highest link ratio(s) from residual sample

drop_low: bool or list of bool (default=None)

Drops lowest link ratio(s) from residual sample

drop_valuation: str or list of str (default=None)

Drops specific valuation periods from residual sample. str must be date convertible.

random_state: int, RandomState instance or None, optional (default=None)

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:

resampled_triangles_: Triangle

A set of triangles represented by each simulation

scale_:

The scale parameter to be used in generating process risk

Examples

Generate ODP bootstrap samples of the RAA sample triangle. The estimator re-samples standardized Pearson residuals to produce n_sims synthetic triangles stacked along the index axis of resampled_triangles_, and exposes the scale parameter scale_ used to generate process risk. random_state and a small n_sims keep the output deterministic and fast.

raa = cl.load_sample('raa')
boot = cl.BootstrapODPSample(n_sims=100, random_state=42).fit(raa)
print(boot.resampled_triangles_.shape)
print(round(float(boot.scale_), 2))

(100, 1, 10, 10)
983.64

Because resampled_triangles_ is itself a Triangle (with the simulation index along the first axis), it can be fed straight into any downstream reserving estimator to obtain a stochastic distribution of ultimates and IBNR. Below, a deterministic chain-ladder is fit on the resampled triangle and the total IBNR is summarised across the 100 simulations.

sims = cl.BootstrapODPSample(
    n_sims=100, random_state=42
).fit_transform(raa)
ibnr = cl.Chainladder().fit(sims).ibnr_.sum('origin')
print(ibnr.shape)
print(round(float(ibnr.mean()), 2))
print(round(float(ibnr.std()), 2))

(100, 1, 1, 1)
51301.13
16149.47

The estimator also supports a leave-one-out sensitivity check on the residual distribution. Setting drop_high=True excludes the highest link ratio in each development column before computing residuals, without making any outlier judgement, so the resulting scale_ measures how influential the column maxima are on the bootstrap. For the RAA triangle this shrinks scale_ from 983.64 to 648.94.

boot_dh = cl.BootstrapODPSample(
    n_sims=100, random_state=42, drop_high=True
).fit(raa)
print(round(float(boot_dh.scale_), 2))

648.94

fit(X, y=None, sample_weight=None)

transform(X)

If X and self are of different shapes, align self to X, else return self.

Parameters:

X: Triangle

The triangle to be transformed

Returns:

X_new: New triangle with transformed attributes.

Inherited Methods

BootstrapODPSample.fit_transform	Fit to data, then transform it.
BootstrapODPSample.get_metadata_routing	Get metadata routing of this object.
BootstrapODPSample.get_params	Get parameters for this estimator.
BootstrapODPSample.pipe
BootstrapODPSample.set_backend	Converts triangle array_backend.
BootstrapODPSample.set_output	Set output container.
BootstrapODPSample.set_params	Set the parameters of this estimator.
BootstrapODPSample.to_json	Serializes triangle object to json format
BootstrapODPSample.to_pickle	Serializes triangle object to pickle.