Expand/Contract All

Exponential Distribution

Page Contents

Exponential Distribution

A random variable ~Y is said to have the #~{exponential distribution} with parameter &beta. if it has the probability density function:

f( ~y ) _ = _ &beta. e^{- &beta.~y} _ _ ~y > 0

We write _ ~Y _ ~ _ M( &beta. )

The exponential distribution is a special case of the Gamma distribution, with &alpha. = 1 . _ I.e. if _ ~Y ~ M( &beta. ) , _ then _ ~Y ~ &Gamma. ( 1 , &beta. ) . _ However little use is made of this fact in calculating the exponential distribution, since the the expnential has one of the few distribution functions that can be written explicitly:

F( ~y ) _ = _ 1 - e^{- &beta.~y}

Random Processes

One of the main uses of the exponential distribution is to model waiting times between successive events in a random ( Poisson ) process.