Statistics - Exponential distribution


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Exponential distribution or negative exponential distribution represents a probability distribution to describe the time between events in a Poisson process. In Poisson process events occur continuously and independently at a constant average rate. Exponential distribution is a particular case of the gamma distribution.

Exponential Distribution

Probability density function

Probability density function of Exponential distribution is given as:

Formula

${ f(x; \lambda ) = } $ $ \begin {cases} \lambda e^{-\lambda x}, & \text{if $x \ge 0 $} \\[7pt] 0, & \text{if $x \lt 0 $} \end{cases} $

Where −

  • ${\lambda}$ = rate parameter.

  • ${x}$ = random variable.

Cumulative distribution function

Cumulative distribution function of Exponential distribution is given as:

Formula

${ F(x; \lambda) = }$ $ \begin {cases} 1- e^{-\lambda x}, & \text{if $x \ge 0 $} \\[7pt] 0, & \text{if $x \lt 0 $} \end{cases} $

Where −

  • ${\lambda}$ = rate parameter.

  • ${x}$ = random variable.



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