distributions.PredictiveDistribution

The joint result every model returns: draws for each simulation (row)

Usage

distributions.PredictiveDistribution()

and component (column), keyed by dimension values.

The mean, quantile, var and tvar methods describe the total over all components, computed from row sums.

Parameters

dims: list of str

Dimension names, e.g. ["lob", "origin"].

components: list of tuple

One key per component, with one int or str per dimension.

draws: list of list of float
One row per simulation, one value per component.

Raises

ValueError
If the keys or the draws do not fit together.

Examples

>>> from prospicio.distributions import PredictiveDistribution
>>> pd = PredictiveDistribution(["line"], [("A",), ("B",)],
...                             [[0.0, 0.0], [0.0, 0.0], [0.0, 100.0], [100.0, 0.0]])
>>> pd.var(0.75)

100.0

>>> pd.marginal(("A",)).var(0.75)

0.0

Attributes

Name Description
dims Dimension names.
n_components Number of components (columns).
n_sims Number of simulations (rows).

dims

Dimension names.

dims: list[str]

n_components

Number of components (columns).

n_components: int

n_sims

Number of simulations (rows).

n_sims: int

Methods

Name Description
aggregate() Sums the components within each simulation over every dimension not
blend() Blends several models’ predictive distributions: simulation i is
blend_by_component() Blends models with weights that differ by component, as
components() Component keys, one tuple per column.
draw_matrix() All draws, one row per simulation.
join() Joins distributions of different models into one portfolio, with a
marginal() One component’s draws, or None if no component has this key.
mean() Mean of the total.
provenance() Where this result came from: model, parameters, seed, stream scheme,
quantile() Quantile of the total.
reorder_groups() Sets the dependence between the groups of dimension dim by
total() The total over all components, one value per simulation.
tvar() Tail value at risk of the total at level p.
var() Value at risk of the total at level p.
variance() Variance of the total.

aggregate()

Sums the components within each simulation over every dimension not

Usage

aggregate(keep)

in keep, keeping the joint structure.

Parameters
keep: list of str
Returns
PredictiveDistribution
Raises
ValueError
If keep names an unknown dimension or repeats one.

blend()

Blends several models’ predictive distributions: simulation i is

Usage

blend(models, weights, seed)

simulation i of model k, with k drawn with probability weights[k] from stream i of seed. Rows stay whole, so sums across components remain coherent. Use weights from stacking_weights or pseudo_bma_weights.

Parameters
models: list of PredictiveDistribution

Same dimensions, components and number of simulations.

weights: list of float

Non-negative, not all zero; normalized.

seed: int
Returns
PredictiveDistribution
Examples
>>> from prospicio.distributions import PredictiveDistribution
>>> a = PredictiveDistribution(["lob"], [("x",)], [[0.0]] * 1000)
>>> b = PredictiveDistribution(["lob"], [("x",)], [[1.0]] * 1000)
>>> mix = PredictiveDistribution.blend([a, b], [0.25, 0.75], seed=7)
>>> abs(mix.mean() - 0.75) < 0.05

True

blend_by_component()

Blends models with weights that differ by component, as

Usage

blend_by_component(models, weights, seed)

HierarchicalStacking gives them: in simulation i every component draws its model from the same uniform against its own cumulative weights, so components with equal weights take the same model and dependence is kept as far as the weights allow.

Parameters
models: list of PredictiveDistribution
weights: list of list of float

One weight vector per component (in components() order), one weight per model.

seed: int
Returns
PredictiveDistribution

components()

Component keys, one tuple per column.

Usage

components()
Returns
list of tuple

draw_matrix()

All draws, one row per simulation.

Usage

draw_matrix()
Returns
list of list of float

join()

Joins distributions of different models into one portfolio, with a

Usage

join(parts, dim, same_simulations=False)

leading dimension dim holding each part’s label, followed by the union of the parts’ dimensions ("" where a part lacks one). Simulation i of the result is simulation i of every part.

Parameters
parts: list of (str, PredictiveDistribution)
dim: str
same_simulations: bool = False
False: the parts were simulated separately, and two with the same seed and stream scheme (which would share random numbers) are refused. True: the parts come from the same scenarios (a cover applied to a reserve) and keep their pairing.
Returns
PredictiveDistribution
Examples
>>> from prospicio.distributions import PredictiveDistribution
>>> a = PredictiveDistribution(["origin"], [(2023,), (2024,)], [[10.0, 20.0], [12.0, 25.0]])
>>> b = PredictiveDistribution(["lob"], [("motor",)], [[50.0], [40.0]])
>>> p = PredictiveDistribution.join([("reserve", a), ("premium", b)], "risk")
>>> p.dims, p.total().draws

([‘risk’, ‘origin’, ‘lob’], [80.0, 77.0])

marginal()

One component’s draws, or None if no component has this key.

Usage

marginal(key)

An origin period is named by its label, as a string or an integer: ("2021",) or (2021,) for a year, ("2021Q3",) for a quarter.

Parameters
key: tuple
Returns
Sampled or None

mean()

Mean of the total.

Usage

mean()
Returns
float

provenance()

Where this result came from: model, parameters, seed, stream scheme,

Usage

provenance()

crate versions and input hash.

Returns
dict

quantile()

Quantile of the total.

Usage

quantile(p)
Parameters
p: float
Returns
float
Raises
ValueError
If p is outside [0, 1].

reorder_groups()

Sets the dependence between the groups of dimension dim by

Usage

reorder_groups(dim, correlation, seed)

Iman–Conover on the groups’ totals, moving each group’s simulations as whole rows: every group keeps its distribution and internal joint structure, and the group totals take a rank correlation close to correlation.

Parameters
dim: str
correlation: list of list of float

One row and column per group, in order of first appearance.

seed: int
Returns
PredictiveDistribution

total()

The total over all components, one value per simulation.

Usage

total()
Returns
Sampled

tvar()

Tail value at risk of the total at level p.

Usage

tvar(p)
Parameters
p: float
Returns
float
Raises
ValueError
If p is outside [0, 1].

var()

Value at risk of the total at level p.

Usage

var(p)
Parameters
p: float
Returns
float
Raises
ValueError
If p is outside [0, 1].

variance()

Variance of the total.

Usage

variance()
Returns
float