Difference between revisions of "Category:Cumulative distribution functions"

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[[category:Analytic Distribution Functions]]
 
[[category:Analytic Distribution Functions]]
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A cumulative distribution function computes the probability that an outcome is less than or equal to the given value. Cumulative functions exist for both [[:category:Continuous distributions|Continuous distributions]] and [[:category:Discrete distributions|Discrete distributions]].  For continuous distributions, these are also sometimes called ''cumulative density functions'' and are equal to the area under the probability density curve lying to the left of the value in question.
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A cumulative distribution function computes the probability that an outcome is less than or equal to the given value. Cumulative functions exist for both [[:category:Continuous distributions|Continuous distributions]] and [[:category:Discrete distributions|Discrete distributions]].  For continuous distributions, these are also sometimes called ''cumulative density functions'' or ''cumulative probability functions'' and are equal to the area under the probability density curve lying to the left of the value in question.
  
 
These functions compute the cumulative probability analytically, without any Monte Carlo sampling error.  
 
These functions compute the cumulative probability analytically, without any Monte Carlo sampling error.  
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Each Cumulative distribution function corresponds to a distribution function, and the naming convention <code>Cum«Dist»</code> is used for the cumulative distribution function corresponding to the distribution function <code>«Dist»(...)</code>. For example, the cumulative probability function corresponding to the [[Normal]]( m, sd ) distribution is [[CumNormal]]( x, m, sd ). In general, they also accept the same parameters, with one addition parameter «x» inserted up front, which is the value that you want to computed the cumulative probability at.
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While these map x to a probability, the [[:category:Inverse cumulative probability functions|Inverse cumulative probability functions]] provide the inverse and map the probability to x.
  
 
In [[Analytica 5.1]] and before, most require you to add the [[Distribution Densities Library]] to your model to use these functions. As of [[Analytica 5.2]], most are provided as built-in functions.
 
In [[Analytica 5.1]] and before, most require you to add the [[Distribution Densities Library]] to your model to use these functions. As of [[Analytica 5.2]], most are provided as built-in functions.

Latest revision as of 23:01, 9 October 2018

A cumulative distribution function computes the probability that an outcome is less than or equal to the given value. Cumulative functions exist for both Continuous distributions and Discrete distributions. For continuous distributions, these are also sometimes called cumulative density functions or cumulative probability functions and are equal to the area under the probability density curve lying to the left of the value in question.

These functions compute the cumulative probability analytically, without any Monte Carlo sampling error.

Each Cumulative distribution function corresponds to a distribution function, and the naming convention Cum«Dist» is used for the cumulative distribution function corresponding to the distribution function «Dist»(...). For example, the cumulative probability function corresponding to the Normal( m, sd ) distribution is CumNormal( x, m, sd ). In general, they also accept the same parameters, with one addition parameter «x» inserted up front, which is the value that you want to computed the cumulative probability at.

While these map x to a probability, the Inverse cumulative probability functions provide the inverse and map the probability to x.

In Analytica 5.1 and before, most require you to add the Distribution Densities Library to your model to use these functions. As of Analytica 5.2, most are provided as built-in functions.