## distributions.Poisson


Poisson claim counts with mean [lam](models.ElasticNet.md#prospicio.models.ElasticNet.lam).


Usage


``` python
distributions.Poisson()
```


## Parameters


`lam: float`  
Mean number of claims; must be finite and non-negative.


## Raises


`ValueError`  
If [lam](models.ElasticNet.md#prospicio.models.ElasticNet.lam) is negative or not finite.


## Examples

``` python
>>> from prospicio.distributions import Poisson
>>> n = Poisson(3.0)
>>> round(n.pmf(0), 6)
```

0.049787


## Attributes

| Name | Description |
|----|----|
| [lam](#lam) | The mean number of claims. |

------------------------------------------------------------------------


#### lam


The mean number of claims.


`lam: float`


## Methods

| Name | Description |
|----|----|
| [cdf()](#cdf) | `P(N <= k)`. |
| [mean()](#mean) | Mean of the claim count. |
| [pmf()](#pmf) | `P(N = k)`. |
| [quantile()](#quantile) | Smallest `k` with `P(N <= k) >= p`. |
| [sample()](#sample) | [n](distributions.Binomial.md#prospicio.distributions.Binomial.n) claim counts from stream `stream` of the generator keyed by |
| [variance()](#variance) | Variance of the claim count. |

------------------------------------------------------------------------


#### cdf()


`P(N <= k)`.


Usage


``` python
cdf(k)
```


##### Parameters


`k: int`  


##### Returns


`float`  


------------------------------------------------------------------------


#### mean()


Mean of the claim count.


Usage


``` python
mean()
```


##### Returns


`float`  


------------------------------------------------------------------------


#### pmf()


`P(N = k)`.


Usage


``` python
pmf(k)
```


##### Parameters


`k: int`  


##### Returns


`float`  


------------------------------------------------------------------------


#### quantile()


Smallest `k` with `P(N <= k) >= p`.


Usage


``` python
quantile(p)
```


##### Parameters


`p: float`  
Probability in `[0, 1)`.


##### Returns


`int`  


##### Raises


`ValueError`  
If [p](models.Elpd.md#prospicio.models.Elpd.p) is outside `[0, 1]`.


------------------------------------------------------------------------


#### sample()


[n](distributions.Binomial.md#prospicio.distributions.Binomial.n) claim counts from stream `stream` of the generator keyed by


Usage


``` python
sample(n, seed, stream=0)
```


[seed](aggregate.EventSet.md#prospicio.aggregate.EventSet.seed).


##### Parameters


`n: int`  

`seed: int`  

`stream: int = ``0`  


##### Returns


`list of int`  


------------------------------------------------------------------------


#### variance()


Variance of the claim count.


Usage


``` python
variance()
```


##### Returns


`float`