reserving.Mack

Mack’s distribution-free chain ladder: the chain-ladder projection plus

Usage

reserving.Mack()

the standard error of each origin’s reserve and of the total, split into process and parameter risk (Mack 1993, 1999).

A tail other than 1 is one more development step, from the oldest age to ultimate, with its own sigma and standard error, as R ChainLadder’s MackChainLadder(tail = ...); unless given, both are extrapolated log-linearly. Every origin, the oldest included, carries the tail’s risk. A tail below 1 follows chainladder-python: it scales the ultimates and carries the risk read where a tail of 1.001 would be. R’s MackChainLadder ignores a tail below 1 altogether.

Parameters

average: (volume, simple, regression) = "volume"
sigma_interpolation: (log - linear, mack) = "log-linear"
tail: (float, TailConstant, TailCurve, TailBondy or TailLogLinear): As ChainLadder; no tail by default.
tail_sigma: float: The tail’s sigma (R’s tail.sigma); extrapolated if not given. Unused when the tail factor is 1.
tail_std_err: float: The tail factor’s standard error (R’s tail.se); extrapolated if not given. Unused when the tail factor is 1.

Examples

>>> from prospicio.reserving import Mack, Triangle
>>> tri = Triangle.from_long(
...     [2020] * 4 + [2021] * 3 + [2022] * 2 + [2023],
...     [12, 24, 36, 48, 12, 24, 36, 12, 24, 12],
...     [100.0, 150.0, 165.0, 170.0, 110.0, 170.0, 180.0, 120.0, 175.0, 130.0],
... )
>>> fit = Mack().fit(tri, "values")
>>> fit.total_standard_error > 0 and fit.standard_error[0] == 0

True

Attributes

Name	Description
average	How link ratios are averaged.
sigma_interpolation	How unestimable variance parameters are filled in.
tail	The tail: a constant factor as a number, otherwise its estimator.
tail_sigma	The given tail sigma, or `None` to extrapolate it.
tail_std_err	The given standard error of the tail factor, or `None` to

average

How link ratios are averaged.

average: str

sigma_interpolation

How unestimable variance parameters are filled in.

sigma_interpolation: str

tail

The tail: a constant factor as a number, otherwise its estimator.

tail: Any

tail_sigma

The given tail sigma, or None to extrapolate it.

tail_sigma: float | None

tail_std_err

The given standard error of the tail factor, or None to

tail_std_err: float | None

extrapolate it.

Methods

Name	Description
fit()	Fits one measure column in every segment of a triangle, each on its

fit()

Fits one measure column in every segment of a triangle, each on its

Usage

fit(triangle, column)

own.

Parameters

triangle: Triangle
column: str

Returns

MackFit

Raises

ValueError: As ChainLadder.fit, and if the triangle has fewer than three ages, a variance parameter can be neither estimated nor interpolated, or the tail’s sigma or standard error can neither be extrapolated nor is given.