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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.
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} $
$ 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} $
$ 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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