## distributions.Grid A distribution on the points `0, step, 2*step, ...`: the discretized Usage ``` python distributions.Grid() ``` representation that FFT and Panjer aggregation work on. ## Parameters `step: float` Grid step; must be positive. `probs: list of float` Probabilities at `0, step, ...`; non-negative, summing to 1. ## Raises `ValueError` If the step is not positive or the probabilities are invalid. ## Examples ``` python >>> from prospicio.distributions import Grid, Lognormal >>> grid, report = Grid.local_moment(Lognormal(7.0, 0.5), 100.0, 200) >>> report.tail_mass < 1e-8 ``` True ## Attributes | Name | Description | |----|----| | [probs](#probs) | Probabilities at `0, step, 2*step, ...`. | | [step](#step) | Grid step. | ------------------------------------------------------------------------ #### probs Probabilities at `0, step, 2*step, ...`. `probs: list[float]` ------------------------------------------------------------------------ #### step Grid step. `step: float` ## Methods | Name | Description | |----|----| | [cdf()](#cdf) | Distribution function `P(X <= x)`. | | [layer()](#layer) | Expected loss to the layer [limit](reinsurance.Layer.md#prospicio.reinsurance.Layer.limit) xs [attachment](reinsurance.Layer.md#prospicio.reinsurance.Layer.attachment). | | [lev()](#lev) | Limited expected value `E[min(X, limit)]`, exact on the grid. | | [local_moment()](#local_moment) | Discretizes a severity by local moment matching on the mean. | | [lower()](#lower) | Discretizes a severity by moving each cell's mass to its left end: a | | [map()](#map) | The distribution of `f(X)` on the same step. | | [mean()](#mean) | Mean of the distribution. | | [quantile()](#quantile) | Smallest grid point [x](pricing.TabulatedCurve.md#prospicio.pricing.TabulatedCurve.x) with `P(X <= x) >= p`. | | [rounding()](#rounding) | Discretizes a severity by rounding each loss to the nearest point. | | [stop_loss()](#stop_loss) | Expected excess `E[max(X - retention, 0)]`, exact on the grid. | | [variance()](#variance) | Variance of the distribution. | ------------------------------------------------------------------------ #### cdf() Distribution function `P(X <= x)`. Usage ``` python cdf(x) ``` ##### Parameters `x: float` ##### Returns `float` ------------------------------------------------------------------------ #### layer() Expected loss to the layer [limit](reinsurance.Layer.md#prospicio.reinsurance.Layer.limit) xs [attachment](reinsurance.Layer.md#prospicio.reinsurance.Layer.attachment). Usage ``` python layer(limit, attachment) ``` ##### Parameters `limit: float` `attachment: float` ##### Returns `float` ------------------------------------------------------------------------ #### lev() Limited expected value `E[min(X, limit)]`, exact on the grid. Usage ``` python lev(limit) ``` ##### Parameters `limit: float` ##### Returns `float` ------------------------------------------------------------------------ #### local_moment() Discretizes a severity by local moment matching on the mean. Usage ``` python local_moment(severity, step, points) ``` ##### Parameters `severity: (Lognormal, Grid, Pareto, PiecewisePareto, LogAffinePareto or GeneralizedPareto)` `step: float` `points: int` ##### Returns `tuple of (Grid, DiscretizationReport)` ##### Raises `ValueError` If [step](distributions.Grid.md#prospicio.distributions.Grid.step) is not positive or [points](aggregate.CompoundReport.md#prospicio.aggregate.CompoundReport.points) is 0. ------------------------------------------------------------------------ #### lower() Discretizes a severity by moving each cell's mass to its left end: a Usage ``` python lower(severity, step, points) ``` stochastic lower bound. ##### Parameters `severity: (Lognormal, Grid, Pareto, PiecewisePareto, LogAffinePareto or GeneralizedPareto)` `step: float` `points: int` ##### Returns `tuple of (Grid, DiscretizationReport)` ##### Raises `ValueError` If [step](distributions.Grid.md#prospicio.distributions.Grid.step) is not positive or [points](aggregate.CompoundReport.md#prospicio.aggregate.CompoundReport.points) is 0. ------------------------------------------------------------------------ #### map() The distribution of `f(X)` on the same step. Usage ``` python map(f) ``` Each point's mass moves to `f(x)`. A value between two points is split between them so its mean is kept, so the mean is always exact and the whole distribution is exact when every value lands on a point. `f` is a Python callable, evaluated once per point with mass. ##### Parameters `f: callable` Maps a loss to a finite, non-negative value. ##### Returns `tuple of (Grid, bool)` The grid and whether every value landed on a grid point. ##### Raises `ValueError` If `f` returns a negative or non-finite value. ##### Examples ``` python >>> from prospicio.distributions import Grid >>> x = Grid(1.0, [0.2, 0.3, 0.3, 0.2]) >>> layer, exact = x.map(lambda v: min(max(v - 1.0, 0.0), 1.0)) >>> layer.probs, exact ``` (\[0.5, 0.5\], True) ------------------------------------------------------------------------ #### mean() Mean of the distribution. Usage ``` python mean() ``` ##### Returns `float` ------------------------------------------------------------------------ #### quantile() Smallest grid point [x](pricing.TabulatedCurve.md#prospicio.pricing.TabulatedCurve.x) with `P(X <= x) >= p`. Usage ``` python quantile(p) ``` ##### Parameters `p: float` ##### Returns `float` ##### Raises `ValueError` If [p](models.Elpd.md#prospicio.models.Elpd.p) is outside `[0, 1]`. ------------------------------------------------------------------------ #### rounding() Discretizes a severity by rounding each loss to the nearest point. Usage ``` python rounding(severity, step, points) ``` ##### Parameters `severity: (Lognormal, Grid, Pareto, PiecewisePareto, LogAffinePareto or GeneralizedPareto)` `step: float` `points: int` ##### Returns `tuple of (Grid, DiscretizationReport)` ##### Raises `ValueError` If [step](distributions.Grid.md#prospicio.distributions.Grid.step) is not positive or [points](aggregate.CompoundReport.md#prospicio.aggregate.CompoundReport.points) is 0. ------------------------------------------------------------------------ #### stop_loss() Expected excess `E[max(X - retention, 0)]`, exact on the grid. Usage ``` python stop_loss(retention) ``` ##### Parameters `retention: float` ##### Returns `float` ------------------------------------------------------------------------ #### variance() Variance of the distribution. Usage ``` python variance() ``` ##### Returns `float`