Statistics/Distributions/Exponential

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Exponential distribution refers to a statistical distribution used to model the time between independent events that happen at a constant average rate λ. Some examples of this distribution are:

  • The distance between one car passing by after the previous one.
  • The rate at which radioactive particles decay.

For the stochastic variable X, probability distribution function of it is:

f_x (x) = \begin{cases} \lambda e^{- \lambda x}, & \mbox{if } x \ge 0 \\ 0, & \mbox{if } x < 0 \end{cases}

and the cumulative distribution function is:

F_x (x) = \begin{cases} 0, & \mbox{if } x < 0 \\ {1 - e^{- \lambda x}}, & \mbox{if } x \ge 0 \end{cases}

Exponential distribution is denoted as X \in \mbox{Exp(m)} , where m is the average number of events within a given time period. So if m=3 per minute, i.e. there are event three events per minute, then λ=1/3, i.e. one event is expected on average to take place every 20 seconds.

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