Difference between revisions of "LogNormal Command"

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;LogNormal( <Mean>, <Standard Deviation>, x )
;LogNormal[ <Mean μ>, <Standard Deviation σ>, x ]
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:Creates cumulative density function (cdf) of [[w:Log-normal distribution|log-normal distribution]] with parameters mean ''μ'' and standard deviation ''σ''.
:Creates probability density function (pdf) of [[w:Log-normal distribution|log-normal distribution]] with parameters ''μ, σ''.
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;LogNormal( <Mean>, <Standard Deviation>, x, <Boolean Cumulative> )
;LogNormal[ <Mean μ>, <Standard Deviation σ>, x, <Boolean Cumulative> ]
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:If ''Cumulative'' is true, creates cumulative density function of log-normal distribution, otherwise creates pdf of log-normal distribution.
:If ''Cumulative'' is true, creates cumulative density function of LogNormal distribution, otherwise creates pdf of log-normal distribution.
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;LogNormal( <Mean>, <Standard Deviation>, <Variable Value> )
;LogNormal[ <Mean μ>, <Standard Deviation σ>, <Variable Value v> ]: Calculates the value of cumulative distribution function of log-normal distribution at ''v'', i.e. the probability ''P(X≤v)'' where ''X'' is a random variable with log-normal distribution given by parameters ''μ, σ''.
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:Calculates the value of cumulative distribution function of log-normal distribution at variable value ''v'', i.e. the probability ''P(X ≤ v)'' where ''X'' is a random variable with log-normal distribution given by parameters mean ''μ'' and standard deviation ''σ''.
 
:{{Note| Returns the probability for a given ''x''-coordinate's value (or area under the log-normal 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 log-normal distribution curve to the left of the given ''x''-coordinate).}}
==CAS Syntax==
 
;LogNormal[ <Mean μ>, <Standard Deviation σ>, <Variable Value v>]
 
:Calculates the value of cumulative distribution function of log-normal distribution at ''v'', i.e. the probability ''P(X≤v)'' where ''X'' is a random variable with log-normal distribution given by parameters ''μ, σ''.
 

Latest revision as of 11:18, 30 July 2019


LogNormal( <Mean>, <Standard Deviation>, x )
Creates cumulative density function (cdf) of log-normal distribution with parameters mean μ and standard deviation σ.
LogNormal( <Mean>, <Standard Deviation>, x, <Boolean Cumulative> )
If Cumulative is true, creates cumulative density function of log-normal distribution, otherwise creates pdf of log-normal distribution.
LogNormal( <Mean>, <Standard Deviation>, <Variable Value> )
Calculates the value of cumulative distribution function of log-normal distribution at variable value v, i.e. the probability P(X ≤ v) where X is a random variable with log-normal distribution given by parameters mean μ and standard deviation σ.
Note: Returns the probability for a given x-coordinate's value (or area under the log-normal distribution curve to the left of the given x-coordinate).
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