## reserving.ClarkFit A fitted Clark LDF or Cape Cod model of every segment of a triangle Usage ``` python reserving.ClarkFit() ``` column. Per-origin lists ([origins](reserving.MackFit.md#prospicio.reserving.MackFit.origins), [latest](reserving.MackFit.md#prospicio.reserving.MackFit.latest), [expected_ultimate](reserving.ClarkFit.md#prospicio.reserving.ClarkFit.expected_ultimate), [ultimate](reserving.MackFit.md#prospicio.reserving.MackFit.ultimate), [reserve](reserving.MackFit.md#prospicio.reserving.MackFit.reserve) and the standard errors) run over the origins of each segment in turn, like the rows of [to_frame()](reserving.MackFit.md#prospicio.reserving.MackFit.to_frame). The fitted parameters and the standard errors of the total need a single-segment fit; for several segments use [totals_frame()](reserving.MackFit.md#prospicio.reserving.MackFit.totals_frame) 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. ## Examples ``` python >>> from prospicio.reserving import ClarkLdf, Triangle >>> rows = [[110.0, 290.0, 370.0, 420.0, 440.0], [95.0, 300.0, 390.0, 425.0], ... [130.0, 320.0, 410.0], [105.0, 305.0], [120.0]] >>> tri = Triangle.from_long( ... [2020 + i for i, row in enumerate(rows) for _ in row], ... [12 * (d + 1) for row in rows for d in range(len(row))], ... [v for row in rows for v in row], ... ) >>> fit = ClarkLdf().fit(tri, "values") >>> len(fit.covariance), fit.elr, fit.growth(float("inf")) ``` (7, None, 1.0) ## Attributes | Name | Description | |----|----| | [chain_ladder](#chain_ladder) | The volume-weighted chain ladder of the same column, with the chain | | [covariance](#covariance) | Covariance of the parameters: the expected ultimates (LDF) or the | | [curve](#curve) | The growth curve. | | [elr](#elr) | Expected loss ratio (Cape Cod), or `None` (LDF). | | [expected_ultimate](#expected_ultimate) | Expected ultimate per origin, developed to infinity: fitted (LDF) | | [exposure](#exposure) | Exposure per origin (Cape Cod), or `None` (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. | | [max_age](#max_age) | Age in months at which development stops; `None` for infinity. | | [n_observations](#n_observations) | Number of observed incremental values fitted; [scale](reserving.ClarkFit.md#prospicio.reserving.ClarkFit.scale) divides by | | [omega](#omega) | Fitted shape of the growth curve. | | [origin_width](#origin_width) | Length of the origin period in months; ages are shifted by half of | | [origins](#origins) | Origin period of each per-origin value. | | [parameter_risk](#parameter_risk) | Parameter standard error per origin. | | [process_risk](#process_risk) | Process standard error per origin. | | [reserve](#reserve) | Reserve per origin. | | [scale](#scale) | Over-dispersion `sigma**2`: squared Pearson residuals over the | | [standard_error](#standard_error) | Standard error per origin: `sqrt(process**2 + parameter**2)`. | | [theta](#theta) | Fitted scale of the growth curve, in months. | | [total_parameter_risk](#total_parameter_risk) | Parameter standard error of the total reserve, with the covariance | | [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) | Standard error of the total reserve. | | [total_ultimate](#total_ultimate) | Total ultimate across segments and origins. | | [ultimate](#ultimate) | Ultimate per origin: the latest value plus the reserve. | ------------------------------------------------------------------------ #### chain_ladder The volume-weighted chain ladder of the same column, with the chain `chain_ladder: ChainLadderFit` ladder's ultimate. ------------------------------------------------------------------------ #### covariance Covariance of the parameters: the expected ultimates (LDF) or the `covariance: list[list[float]]` expected loss ratio (Cape Cod), then [omega](reserving.ClarkFit.md#prospicio.reserving.ClarkFit.omega) and [theta](reserving.ClarkFit.md#prospicio.reserving.ClarkFit.theta). NaN if the Fisher information is singular. ------------------------------------------------------------------------ #### curve The growth curve. `curve: str` ------------------------------------------------------------------------ #### elr Expected loss ratio (Cape Cod), or `None` (LDF). `elr: float | None` ------------------------------------------------------------------------ #### expected_ultimate Expected ultimate per origin, developed to infinity: fitted (LDF) `expected_ultimate: list[float]` or `elr * exposure` (Cape Cod). ------------------------------------------------------------------------ #### exposure Exposure per origin (Cape Cod), or `None` (LDF). `exposure: list[float] | None` ------------------------------------------------------------------------ #### 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]` ------------------------------------------------------------------------ #### max_age Age in months at which development stops; `None` for infinity. `max_age: float | None` ------------------------------------------------------------------------ #### n_observations Number of observed incremental values fitted; [scale](reserving.ClarkFit.md#prospicio.reserving.ClarkFit.scale) divides by `n_observations: int` this less the number of parameters. ------------------------------------------------------------------------ #### omega Fitted shape of the growth curve. `omega: float` ------------------------------------------------------------------------ #### origin_width Length of the origin period in months; ages are shifted by half of `origin_width: float` it to the average date of loss. ------------------------------------------------------------------------ #### origins Origin period of each per-origin value. `origins: list[str]` ------------------------------------------------------------------------ #### parameter_risk Parameter 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]` ------------------------------------------------------------------------ #### scale Over-dispersion `sigma**2`: squared Pearson residuals over the `scale: float` observed incremental values less the number of parameters. ------------------------------------------------------------------------ #### standard_error Standard error per origin: `sqrt(process**2 + parameter**2)`. `standard_error: list[float]` ------------------------------------------------------------------------ #### theta Fitted scale of the growth curve, in months. `theta: float` ------------------------------------------------------------------------ #### total_parameter_risk Parameter standard error of the total reserve, with the covariance `total_parameter_risk: float` between origins. ------------------------------------------------------------------------ #### 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 Standard error of the total reserve. `total_standard_error: float` ------------------------------------------------------------------------ #### total_ultimate Total ultimate across segments and origins. `total_ultimate: float` ------------------------------------------------------------------------ #### ultimate Ultimate per origin: the latest value plus the reserve. `ultimate: list[float]` ## Methods | Name | Description | |----|----| | [growth()](#growth) | Share of the expected ultimate developed by a development age. | | [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 | ------------------------------------------------------------------------ #### growth() Share of the expected ultimate developed by a development age. Usage ``` python growth(age) ``` ##### Parameters `age: float` Development age in months, before the shift to the average date of loss; `inf` gives 1. ##### Returns `float` ------------------------------------------------------------------------ #### 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 `ClarkFit` ------------------------------------------------------------------------ #### 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), (Cape Cod) [exposure](reserving.ClarkFit.md#prospicio.reserving.ClarkFit.exposure), [expected_ultimate](reserving.ClarkFit.md#prospicio.reserving.ClarkFit.expected_ultimate), [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), 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, and its [omega](reserving.ClarkFit.md#prospicio.reserving.ClarkFit.omega), [theta](reserving.ClarkFit.md#prospicio.reserving.ClarkFit.theta), [scale](reserving.ClarkFit.md#prospicio.reserving.ClarkFit.scale) and (Cape Cod) [elr](reserving.ClarkFit.md#prospicio.reserving.ClarkFit.elr). Needs pandas. ##### Returns `pandas.DataFrame`