Exponential

Represents the time between events in a Poisson process, where events occur continuously and independently at a constant average rate.

Don't get confused with Poisson distribution! One measures how many events happen in a given time frame, and the other measures the time between two independed events.

Create a new Exponential distribution

Exponential X = Exponential(lambda); 

creates a continuous Exponential probability distribution.

Distribution properties:

Property	Type/Return type	Description
lambda (λ)	double	Events occur continuously and independently at a constant average rate.
E()	double	Returns the expected value of average time between two events.
D()	double	Represents variance, that measures the spread of dispersion of the random variable around its expected value E(X).
P(int k)	double	The cumulative distribution function: P(X < k)

In continuous probability distributions, P(X = k) = 0.

Example

Example of a exponential distribution

//Example: The average number of clients is 15 students per hour. What is the 
//probability that you will have to wait not more than 3 minutes for a client 
//to appear?
double lambda = 0.25; //15 students per hour -> 1 client per 4 minutes. 
Exponential X = Exponential(lambda);
std::cout << X.P(3) << std::endl; //0.527633

Common errors

Exponential X = Exponential(0.125); 
std::cout << X.P(-1) << std::endl; //Error: Number of events cannot be less than 0.  

Good to know: k cannot be negative.