# What is the difference between Poisson Distribution and Exponential Distribution?

##### 1 Answer

The Poisson distribution models "rare" events; the exponential distribution models distributions of data that are skewed to the right.

#### Explanation:

The **Poisson probability distribution** often provides a good model for the probability distribution of the number of

Examples include car/industrial accidents, telephone calls handled by a switchboard in a time interval, number of radioactive particles that decay in a particular time period, etc.

A random variable **if and only if**

#p(y)=(lambda^y)/(y!)e^(-lambda)" "y=0,1,2,...,lambda>0#

Where

The **exponential probability distribution** is actually a specific case of the **gamma probability distribution**.

The gamma density function does a sufficient job of modeling the populations associated with random variables that are always nonnegative and yield distributions of data that are skewed (non symmetric) to the right.

A random variable **if and only if** the density function of

#f(y)=(y^(alpha-1)e^(-y)/(beta))/(beta^(alpha)Gamma(alpha))#

and zero elsewhere, where

#Gamma(alpha)=int_0^(oo)y^(alpha-1)e^(-y)dy#

A random variable **if and only if** the density function of

#f(y)=1/(beta)e^(-y/beta)," "0 <= y < oo#

and zero elsewhere.

Essentially, the exponential distribution *is* the gamma distribution, just with