## reserving.MackFit A fitted Mack model of every segment: the chain-ladder fields, plus Usage ``` python reserving.MackFit() ``` standard errors of each origin's reserve and of each segment's total. Per-origin lists run over the origins of each segment in turn, like the rows of [to_frame()](reserving.MackFit.md#prospicio.reserving.MackFit.to_frame). Per-age lists, the tail and the totals' standard errors need a single-segment fit; for several segments use [development_frame()](reserving.MackFit.md#prospicio.reserving.MackFit.development_frame), [totals_frame()](reserving.MackFit.md#prospicio.reserving.MackFit.totals_frame) (the totals' standard errors and the tail) or `segment(...)`. [total_ultimate](reserving.MackFit.md#prospicio.reserving.MackFit.total_ultimate) and [total_reserve](reserving.MackFit.md#prospicio.reserving.MackFit.total_reserve) sum over every segment. ## Attributes | Name | Description | |----|----| | [cdf](#cdf) | Age-to-ultimate factors, including the tail. | | [chain_ladder](#chain_ladder) | The underlying chain-ladder projection. | | [development](#development) | Development ages in months. | | [estimated_ldf](#estimated_ldf) | Factors as estimated, as [ChainLadderFit.estimated_ldf](reserving.ChainLadderFit.md#prospicio.reserving.ChainLadderFit.estimated_ldf). | | [index](#index) | Label of each segment, as [Triangle.index](reserving.Triangle.md#prospicio.reserving.Triangle.index). | | [keys](#keys) | Names of the triangle's key columns; empty without keys. | | [latest](#latest) | Latest observed cumulative value per origin. | | [ldf](#ldf) | Selected age-to-age factors, as [ChainLadderFit.ldf](reserving.ChainLadderFit.md#prospicio.reserving.ChainLadderFit.ldf). | | [origins](#origins) | Origin period of each per-origin value. | | [parameter_risk](#parameter_risk) | Parameter (estimation) standard error per origin. | | [process_risk](#process_risk) | Process standard error per origin. | | [reserve](#reserve) | Reserve per origin. | | [sigma](#sigma) | Variance parameter of each factor. | | [standard_error](#standard_error) | Mack standard error per origin: `sqrt(process**2 + parameter**2)`. | | [std_err](#std_err) | Standard error of each factor. | | [tail](#tail) | Tail factor from the oldest age to ultimate. | | [tail_attachment_age](#tail_attachment_age) | Age from which [ldf](reserving.MackFit.md#prospicio.reserving.MackFit.ldf) holds the tail's factors, as | | [tail_ldf](#tail_ldf) | Factors past the oldest age, as [ChainLadderFit.tail_ldf](reserving.ChainLadderFit.md#prospicio.reserving.ChainLadderFit.tail_ldf). | | [tail_sigma](#tail_sigma) | The tail's sigma used in the process risk: given, or extrapolated | | [tail_std_err](#tail_std_err) | The tail factor's standard error used in the parameter risk: given, | | [total_cv](#total_cv) | Coefficient of variation of the total reserve. | | [total_parameter_risk](#total_parameter_risk) | Parameter standard error of the total reserve, including the | | [total_process_risk](#total_process_risk) | Process standard error of the total reserve. | | [total_reserve](#total_reserve) | Total reserve across segments and origins. | | [total_standard_error](#total_standard_error) | Mack standard error of the total reserve. | | [total_ultimate](#total_ultimate) | Total ultimate across segments and origins. | | [ultimate](#ultimate) | Projected ultimate per origin. | ------------------------------------------------------------------------ #### cdf Age-to-ultimate factors, including the tail. `cdf: list[float]` ------------------------------------------------------------------------ #### chain_ladder The underlying chain-ladder projection. `chain_ladder: ChainLadderFit` ------------------------------------------------------------------------ #### development Development ages in months. `development: list[int]` ------------------------------------------------------------------------ #### estimated_ldf Factors as estimated, as [ChainLadderFit.estimated_ldf](reserving.ChainLadderFit.md#prospicio.reserving.ChainLadderFit.estimated_ldf). `estimated_ldf: list[float]` ------------------------------------------------------------------------ #### index Label of each segment, as [Triangle.index](reserving.Triangle.md#prospicio.reserving.Triangle.index). `index: list[Any]` ------------------------------------------------------------------------ #### keys Names of the triangle's key columns; empty without keys. `keys: list[str]` ------------------------------------------------------------------------ #### latest Latest observed cumulative value per origin. `latest: list[float]` ------------------------------------------------------------------------ #### ldf Selected age-to-age factors, as [ChainLadderFit.ldf](reserving.ChainLadderFit.md#prospicio.reserving.ChainLadderFit.ldf). `ldf: list[float]` ------------------------------------------------------------------------ #### origins Origin period of each per-origin value. `origins: list[str]` ------------------------------------------------------------------------ #### parameter_risk Parameter (estimation) standard error per origin. `parameter_risk: list[float]` ------------------------------------------------------------------------ #### process_risk Process standard error per origin. `process_risk: list[float]` ------------------------------------------------------------------------ #### reserve Reserve per origin. `reserve: list[float]` ------------------------------------------------------------------------ #### sigma Variance parameter of each factor. `sigma: list[float]` ------------------------------------------------------------------------ #### standard_error Mack standard error per origin: `sqrt(process**2 + parameter**2)`. `standard_error: list[float]` ------------------------------------------------------------------------ #### std_err Standard error of each factor. `std_err: list[float]` ------------------------------------------------------------------------ #### tail Tail factor from the oldest age to ultimate. `tail: float` ------------------------------------------------------------------------ #### tail_attachment_age Age from which [ldf](reserving.MackFit.md#prospicio.reserving.MackFit.ldf) holds the tail's factors, as `tail_attachment_age: int` [ChainLadderFit.tail_attachment_age](reserving.ChainLadderFit.md#prospicio.reserving.ChainLadderFit.tail_attachment_age). ------------------------------------------------------------------------ #### tail_ldf Factors past the oldest age, as [ChainLadderFit.tail_ldf](reserving.ChainLadderFit.md#prospicio.reserving.ChainLadderFit.tail_ldf). `tail_ldf: list[float]` ------------------------------------------------------------------------ #### tail_sigma The tail's sigma used in the process risk: given, or extrapolated `tail_sigma: float` log-linearly; 0 without a tail (a factor of 1). ------------------------------------------------------------------------ #### tail_std_err The tail factor's standard error used in the parameter risk: given, `tail_std_err: float` or extrapolated log-linearly; 0 without a tail (a factor of 1). ------------------------------------------------------------------------ #### total_cv Coefficient of variation of the total reserve. `total_cv: float` ------------------------------------------------------------------------ #### total_parameter_risk Parameter standard error of the total reserve, including the `total_parameter_risk: float` correlation between origins that share estimated factors. ------------------------------------------------------------------------ #### total_process_risk Process standard error of the total reserve. `total_process_risk: float` ------------------------------------------------------------------------ #### total_reserve Total reserve across segments and origins. `total_reserve: float` ------------------------------------------------------------------------ #### total_standard_error Mack standard error of the total reserve. `total_standard_error: float` ------------------------------------------------------------------------ #### total_ultimate Total ultimate across segments and origins. `total_ultimate: float` ------------------------------------------------------------------------ #### ultimate Projected ultimate per origin. `ultimate: list[float]` ## Methods | Name | Description | |----|----| | [claims_development_result()](#claims_development_result) | Merz and Wüthrich's (2008) one-year view: the standard error of the | | [development_frame()](#development_frame) | One row per segment and age, as [ChainLadderFit.development_frame](reserving.ChainLadderFit.md#prospicio.reserving.ChainLadderFit.development_frame). | | [segment()](#segment) | The fit of one segment, chosen by key values as | | [to_frame()](#to_frame) | One row per segment and origin: the key columns, `origin`, | | [totals_frame()](#totals_frame) | One row per segment: the key columns, the segment's total | ------------------------------------------------------------------------ #### claims_development_result() Merz and Wüthrich's (2008) one-year view: the standard error of the Usage ``` python claims_development_result() ``` claims development result of each origin and in total, in the next calendar year and in every later one, as R ChainLadder's `CDR(MackChainLadder(x), dev = "all")`. ##### Returns `ClaimsDevelopmentResult` ##### Raises `ValueError` If the fit has several segments (use `segment(...)`), the factors are not volume-weighted, the fit has a tail (a factor other than 1, or one that replaces estimated factors), or the latest values do not lie on one calendar diagonal with one new origin per period. ------------------------------------------------------------------------ #### development_frame() One row per segment and age, as [ChainLadderFit.development_frame](reserving.ChainLadderFit.md#prospicio.reserving.ChainLadderFit.development_frame). Usage ``` python development_frame() ``` Needs pandas. ##### Returns `pandas.DataFrame` ------------------------------------------------------------------------ #### segment() The fit of one segment, chosen by key values as Usage ``` python segment(**keys) ``` [ChainLadderFit.segment](reserving.ChainLadderFit.md#prospicio.reserving.ChainLadderFit.segment). ##### Returns `MackFit` ------------------------------------------------------------------------ #### to_frame() One row per segment and origin: the key columns, `origin`, Usage ``` python to_frame() ``` [latest](reserving.MackFit.md#prospicio.reserving.MackFit.latest), [ultimate](reserving.MackFit.md#prospicio.reserving.MackFit.ultimate), [reserve](reserving.MackFit.md#prospicio.reserving.MackFit.reserve), [process_risk](reserving.MackFit.md#prospicio.reserving.MackFit.process_risk), [parameter_risk](reserving.MackFit.md#prospicio.reserving.MackFit.parameter_risk) and [standard_error](reserving.MackFit.md#prospicio.reserving.MackFit.standard_error). Needs pandas. ##### Returns `pandas.DataFrame` ------------------------------------------------------------------------ #### totals_frame() One row per segment: the key columns, the segment's total Usage ``` python totals_frame() ``` [latest](reserving.MackFit.md#prospicio.reserving.MackFit.latest), [ultimate](reserving.MackFit.md#prospicio.reserving.MackFit.ultimate) and [reserve](reserving.MackFit.md#prospicio.reserving.MackFit.reserve), and the [process_risk](reserving.MackFit.md#prospicio.reserving.MackFit.process_risk), [parameter_risk](reserving.MackFit.md#prospicio.reserving.MackFit.parameter_risk) and [standard_error](reserving.MackFit.md#prospicio.reserving.MackFit.standard_error) of its total reserve. Needs pandas. ##### Returns `pandas.DataFrame`