Statistics Tutorial
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Exponential distribution
Statistics - Exponential distribution
Exponential distribution or negative exponential distribution represents a probabipty 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.
Probabipty density function
Probabipty density function of Exponential distribution is given as:
Formula
${ f(x; lambda ) = } $ $ egin {cases} lambda e^{-lambda x}, & ext{if $x ge 0 $} \[7pt] 0, & ext{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
${ F(x; lambda) = }$ $ egin {cases} 1- e^{-lambda x}, & ext{if $x ge 0 $} \[7pt] 0, & ext{if $x lt 0 $} end{cases} $Where −
${lambda}$ = rate parameter.
${x}$ = random variable.