Difference between revisions of "Cauchy Command"
From GeoGebra Manual
m (Text replace - "<div class="box info"> 48px|left This page is part of the official manual for print and pdf. For structural reasons normal users can't edit this page. If you found any errors on this page please contact ) |
|||
| Line 1: | Line 1: | ||
<noinclude>{{Manual Page|version=4.2}}</noinclude> | <noinclude>{{Manual Page|version=4.2}}</noinclude> | ||
{{command|cas=true|probability}} | {{command|cas=true|probability}} | ||
| − | ;Cauchy[ <Median | + | ;Cauchy[ <Median>, <Scale>, x ] |
:Creates probability density function (pdf) of [[w:Cauchy distribution|Cauchy distribution]]. | :Creates probability density function (pdf) of [[w:Cauchy distribution|Cauchy distribution]]. | ||
| − | ;Cauchy[ <Median | + | ;Cauchy[ <Median>, <Scale>, x, <Boolean Cumulative>] |
:If ''Cumulative'' is true, creates cumulative distribution function of Cauchy distribution, otherwise creates pdf of Cauchy distribution. | :If ''Cumulative'' is true, creates cumulative distribution function of Cauchy distribution, otherwise creates pdf of Cauchy distribution. | ||
| − | ;Cauchy[ <Median | + | ;Cauchy[ <Median>, <Scale>, <Variable Value> ] |
| − | :Calculates the value of cumulative distribution function of Cauchy distribution at ''v'', i.e. the probability ''P( | + | :Calculates the value of cumulative distribution function of Cauchy distribution at ''Variable Value'' ''v'', i.e. the probability ''P(X ≤ v)'' where ''X'' is a random variable with Cauchy given by parameters ''Median'' and ''Scale''. |
:{{note| Returns the probability for a given ''x''-coordinate's value (or area under the Cauchy 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 Cauchy distribution curve to the left of the given ''x''-coordinate).}} | ||
==CAS Syntax== | ==CAS Syntax== | ||
| − | ;Cauchy[ <Median | + | ;Cauchy[ <Median>, <Scale>, <Variable Value> ] |
| − | :Calculates the value of cumulative distribution function of Cauchy distribution at ''v'', i.e. the probability ''P( | + | :Calculates the value of cumulative distribution function of Cauchy distribution at ''Variable Value'' ''v'', i.e. the probability ''P(X ≤ v)'' where ''X'' is a random variable with Cauchy given by parameters ''Median'' and ''Scale''. |
:{{example| 1=<div><code><nowiki>Cauchy[1, 2, 3]</nowiki></code> yields ''<math>\frac{3}{4}</math>''.</div>}} | :{{example| 1=<div><code><nowiki>Cauchy[1, 2, 3]</nowiki></code> yields ''<math>\frac{3}{4}</math>''.</div>}} | ||
Revision as of 12:12, 26 April 2013
- Cauchy[ <Median>, <Scale>, x ]
- Creates probability density function (pdf) of Cauchy distribution.
- Cauchy[ <Median>, <Scale>, x, <Boolean Cumulative>]
- If Cumulative is true, creates cumulative distribution function of Cauchy distribution, otherwise creates pdf of Cauchy distribution.
- Cauchy[ <Median>, <Scale>, <Variable Value> ]
- Calculates the value of cumulative distribution function of Cauchy distribution at Variable Value v, i.e. the probability P(X ≤ v) where X is a random variable with Cauchy given by parameters Median and Scale.
- Note: Returns the probability for a given x-coordinate's value (or area under the Cauchy distribution curve to the left of the given x-coordinate).
CAS Syntax
- Cauchy[ <Median>, <Scale>, <Variable Value> ]
- Calculates the value of cumulative distribution function of Cauchy distribution at Variable Value v, i.e. the probability P(X ≤ v) where X is a random variable with Cauchy given by parameters Median and Scale.
- Example:
Cauchy[1, 2, 3]yields \frac{3}{4}.
