Difference between revisions of "Erlang Command"

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<noinclude>{{Manual Page|version=5.0}}</noinclude>{{command|probability}}
{{command|probability}}
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;Erlang( <Shape>, <Rate>, x )
;Erlang[ <Shape>, <Rate>, x ]
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:Creates cumulative density function (cdf) of [[w:Erlang distribution|Erlang distribution]] with parameters shape ''k'' and rate ''λ''.
:Creates probability density function (pdf) of [[w:Erlang distribution|Erlang distribution]] with parameters shape ''k'' and rate ''λ''.
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;Erlang( <Shape>, <Rate>, x, <Boolean Cumulative> )
;Erlang[ <Shape>, <Rate>, x, <Boolean Cumulative> ]
 
 
:If ''Cumulative'' is true, creates cumulative distribution function of Erlang distribution, otherwise creates pdf of Erlang distribution.
 
:If ''Cumulative'' is true, creates cumulative distribution function of Erlang distribution, otherwise creates pdf of Erlang distribution.
;Erlang[ <Shape>, <Rate>, <Variable Value> ]: Calculates the value of cumulative distribution function of Erlang distribution at variable value ''v'', i.e. the probability ''P(X ≤ v)'' where ''X'' is a random variable with Erlang distribution given by parameters shape ''k'' and rate ''λ''.
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;Erlang( <Shape>, <Rate>, <Variable Value> ): Calculates the value of cumulative distribution function of Erlang distribution at variable value ''v'', i.e. the probability ''P(X ≤ v)'' where ''X'' is a random variable with Erlang distribution given by parameters shape ''k'' and rate ''λ''.
:{{Note| Returns the probability for a given ''x''-coordinate's value (or area under the Erlang distribution curve to the left of the given ''x''-coordinate).}}
 
==CAS Syntax==
 
;Erlang[ <Shape>, <Rate>, x ]
 
:Creates probability density function (pdf) of [[w:Erlang distribution|Erlang distribution]] with parameters shape ''k'' and rate ''λ''.
 
;Erlang[ <Shape>, <Rate>, x, <Boolean Cumulative> ]
 
:If ''Cumulative'' is true, creates cumulative distribution function of Erlang distribution, otherwise creates pdf of Erlang distribution.
 
;Erlang[ <Shape>, <Rate>, <Variable Value> ]: Calculates the value of cumulative distribution function of Erlang distribution at variable value ''v'', i.e. the probability ''P(X ≤ v)'' where ''X'' is a random variable with Erlang distribution given by parameters shape ''k'' and rate ''λ''.
 
 
:{{Note| Returns the probability for a given ''x''-coordinate's value (or area under the Erlang distribution curve to the left of the given ''x''-coordinate).}}
 
:{{Note| Returns the probability for a given ''x''-coordinate's value (or area under the Erlang distribution curve to the left of the given ''x''-coordinate).}}

Latest revision as of 11:16, 30 July 2019


Erlang( <Shape>, <Rate>, x )
Creates cumulative density function (cdf) of Erlang distribution with parameters shape k and rate λ.
Erlang( <Shape>, <Rate>, x, <Boolean Cumulative> )
If Cumulative is true, creates cumulative distribution function of Erlang distribution, otherwise creates pdf of Erlang distribution.
Erlang( <Shape>, <Rate>, <Variable Value> )
Calculates the value of cumulative distribution function of Erlang distribution at variable value v, i.e. the probability P(X ≤ v) where X is a random variable with Erlang distribution given by parameters shape k and rate λ.
Note: Returns the probability for a given x-coordinate's value (or area under the Erlang distribution curve to the left of the given x-coordinate).
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