## distributions.local_pareto_to_piecewise()


Converts the local Pareto distribution with local alpha `alpha(x)`


Usage


``` python
distributions.local_pareto_to_piecewise(
    t, alpha, rel_tolerance=0.0001, stop_survival=1e-09, stop_at=Ellipsis
)
```


above [t](distributions.Pareto.md#prospicio.distributions.Pareto.t) to a piecewise Pareto that matches its survival function exactly at the thresholds and within `rel_tolerance` between them.


## Parameters


`t: float`  
Threshold; `P(X > x) = 1` below it.

`alpha: callable`  
`alpha(x) -> float`, finite and non-negative, positive where the conversion stops.

`rel_tolerance: float = ``1e-4`  

`stop_survival: float = ``1e-9`  
Stop once the survival function falls below this.

`stop_at: float = inf`  
Stop at this amount.


## Returns


`tuple of (PiecewisePareto, float, float)`  
The approximation, the largest relative error found, and where the approximated range ends (the last alpha continues above it).


## Examples

``` python
>>> import math
>>> from prospicio.distributions import local_pareto_to_piecewise
>>> pp, err, end = local_pareto_to_piecewise(1000.0, lambda x: 1.5 + 0.3 * math.log(x / 1000.0))
>>> err <= 1e-4
```

True