Statistics - Exponential distribution
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.
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.
Advertisements