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Exponential distribution
  • 时间:2024-11-03

Statistics - Exponential distribution


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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.

Exponential 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.

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