RiskPoisson

Description

 

RiskPoisson(lambda) specifies a Poisson distribution parameter lambda, the mean.  The Poisson distribution is a discrete distribution that returns only nonnegative integer values. It is often used to model the number of events that occur in a given time period where the rate of occurrences is constant. For example, it is often used in insurance modeling and financial markets to model the number of events (e.g. earthquakes, fires, stock market crashes) that might occur in a given period. It can also be applied to processes over other domains, e.g., spatial). 

 

Examples

 

RiskPoisson(5) returns a Poisson distribution with mean 5.

RiskPoisson(A6) returns a Poisson distribution with mean taken from cell A6.

 

Guidelines

lambda must be positive.

Parameters

λ mean number of successes      continuous λ > 0 *

*λ = 0 is supported but it returns a degenerate distribution with x = 0.

Domain

0 ≤ x < +∞ discrete integers

Mass and Cumulative Distribution Functions

 

 

Mean

λ

Variance

λ

Skewness

 

Kurtosis

 

Mode

(bimodal) λ and λ-1 (bimodal) if λ is an integer
(unimodal) largest integer less than λ otherwise

Examples