# Pois: Poisson Distribution In Distributacalcul: Probability Distribution Functions

## Description

Poisson distribution with rate parameter lambda.

## Usage

 ``` 1 2 3 4 5 6 7 8 9 10 11``` ```expValPois(lambda) varPois(lambda) expValTruncPois(d, lambda, k0, less.than.d = TRUE) TVatRPois(kap, lambda, k0) mgfPois(t, lambda) pgfPois(t, lambda) ```

## Arguments

 `lambda` Rate parameter lambda. `d` cut-off value. `k0` point up to which to sum the distribution for the approximation. `less.than.d` logical; if `TRUE` (default) truncated mean for values <= d, otherwise, for values > d. `kap` probability. `t` t.

## Details

The Poisson distribution with rate parameter lam has probability mass function :

Pr(X = k) = (lam^k e^(-lam)) / k!

for k = 0, 1, 2, ..., and lam > 0

## Value

Function :

• `expValPois` gives the expected value.

• `varPois` gives the variance.

• `expValTruncPois` gives the truncated mean.

• `TVatRPois` gives the Tail Value-at-Risk.

• `mgfPois` gives the moment generating function (MGF).

• `pgfPois` gives the probability generating function (PGF).

Invalid parameter values will return an error detailing which parameter is problematic.

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12``` ```expValPois(lambda = 3) varPois(lambda = 3) expValTruncPois(d = 0, lambda = 2, k0 = 2E2, less.than.d = FALSE) expValTruncPois(d = 2, lambda = 2, k0 = 2E2, less.than.d = TRUE) TVatRPois(kap = 0.8, lambda = 3, k0 = 2E2) mgfPois(t = 1, lambda = 3) pgfPois(t = 1, lambda = 3) ```

Distributacalcul documentation built on Sept. 13, 2020, 5:19 p.m.