Exponential distribution
The exponential distribution is a continuous probability distribution with probability density function:
- p(t) = 0 for t<0
- p(t) = exp(-t/λ)/λ for t ≥ 0
where λ > 0 is a parameter of the distribution.
The distribution is useful in a situation where an object is initially in state A and can change to state B with constant probability per unit time, equal to 1/λ. A random variable following the exponential distribution describes the time at which the state switches. Therefore, the integral from 0 to T over p is the probability that at time T the object is in state B.
Examples of variables that are exponentially distributed:
- the time until you have your next car accident
- the time until you get your next phone call
- the distance between mutations on a DNA strand
- the distance between roadkill
The expected value and the standard deviation of a random variable following the exponential distribution are both equal to λ
The shape of the probability density function for λ=5 is shown below:
See also: statistics