Difference between revisions of "Documentation/How Tos/Calc: BETADIST function"
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− | __NOTOC__ | + | {{DISPLAYTITLE:BETADIST function}} |
+ | {{Documentation/CalcFunc StatisticalTOC | ||
+ | |ShowPrevNext=block | ||
+ | |PrevPage=Documentation/How_Tos/Calc:_B_function | ||
+ | |NextPage=Documentation/How_Tos/Calc:_BETAINV_function | ||
+ | }}__NOTOC__ | ||
== BETADIST == | == BETADIST == | ||
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The beta distribution is a family of continuous probability distributions, where <tt>'''α'''</tt> and <tt>'''β'''</tt> are parameters controlling the shape of the distribution. | The beta distribution is a family of continuous probability distributions, where <tt>'''α'''</tt> and <tt>'''β'''</tt> are parameters controlling the shape of the distribution. | ||
+ | |||
+ | <tt>'''x'''</tt> is the number, at which you will evaluate the Beta distribution. | ||
The parameters <tt>'''a'''</tt> and <tt>'''b'''</tt> are lower and upper bounds of the distribution. You can interpret the value a as ''location'' and the value b−a as ''scale''. | The parameters <tt>'''a'''</tt> and <tt>'''b'''</tt> are lower and upper bounds of the distribution. You can interpret the value a as ''location'' and the value b−a as ''scale''. | ||
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<tt>'''a'''</tt> and <tt>'''b'''</tt> are optional parameters which default (if omitted) to <tt>'''0'''</tt> and <tt>'''1'''</tt>. | <tt>'''a'''</tt> and <tt>'''b'''</tt> are optional parameters which default (if omitted) to <tt>'''0'''</tt> and <tt>'''1'''</tt>. | ||
− | <tt>'''cumulative'''</tt> is an optional parameter which defaults to TRUE() if omitted. | + | <tt>'''cumulative'''</tt> is an optional, logical parameter which defaults to TRUE() if omitted. |
Before OOo version 3.1 the parameter ''cumulative'' doesn't exist and only the cumulative probability function is calculated. | Before OOo version 3.1 the parameter ''cumulative'' doesn't exist and only the cumulative probability function is calculated. | ||
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Constraints: | Constraints: | ||
# α > 0 , β > 0 , a < b | # α > 0 , β > 0 , a < b | ||
− | # If α < 1, | + | # If α < 1, then the density function has a pole at x = a. |
− | # If β < 1, | + | # If β < 1, then the density function has a pole at x = b. |
=== Semantic === | === Semantic === | ||
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=== Example === | === Example === | ||
− | + | {| | |
− | + | |<tt>'''BETADIST(1;5;3;-2;4;FALSE())</tt> | |
− | <tt>'''BETADIST(1;5;3;-2;4;FALSE())</tt> | + | |
: returns approximately 0.273 | : returns approximately 0.273 | ||
+ | |[[Image:BetaDistributionDensityLocationScale.png|Graphs of Beta distribution density functions using parameter a and b]] | ||
+ | |} | ||
− | + | {| | |
− | + | |<tt>'''BETADIST(0.2;0.7;4;0;1;FALSE())</tt> | |
− | <tt>'''BETADIST(0.2;0.7;4;0;1;FALSE())</tt> | + | |
: returns approximately 1.644 | : returns approximately 1.644 | ||
+ | |[[Image:BetaDistributionDensityNormal.png|Graphs of Beta distribution density functions with borders 0 and 1]] | ||
+ | |} | ||
− | |||
− | <tt>'''BETADIST(1;1;0.5;0;1;FALSE())</tt> | + | {| |
− | : returns '' | + | |<tt>'''BETADIST(1;1;0.5;0;1;FALSE())</tt> |
+ | : returns ''Invalid argument'' because there is a pole | ||
<tt>'''BETADIST(1.1;1;0.5;0;1;FALSE())</tt> | <tt>'''BETADIST(1.1;1;0.5;0;1;FALSE())</tt> | ||
: returns 0 | : returns 0 | ||
+ | |[[Image:BetaDistributionDensitySpecial.png|Graphs of Beta distribution density functions with alpha=1]] | ||
+ | |} | ||
+ | |||
+ | {| | ||
+ | |<tt>'''BETADIST(1;5;3;-2;4;TRUE())</tt> | ||
+ | : returns approximately 0.227 | ||
+ | call before version 3.1: <tt>'''BETADIST(1;5;3;-2;4)</tt> | ||
+ | |[[Image:BetaDistributionCumulativeLocationScale.png|Graphs of Beta distribution cumulative functions using parameter a and b]] | ||
+ | |} | ||
+ | |||
+ | {| | ||
+ | |<tt>'''BETADIST(0.2;0.7;4;0;1;TRUE())</tt> | ||
+ | : returns approximately 0.718 | ||
+ | call before version 3.1: <tt>'''BETADIST(0.2;0.7:4;0;1)</tt> | ||
+ | |||
+ | other valid call: <tt>'''BETADIST(0.2;0.7;4)</tt> | ||
+ | |[[Image:BetaDistributionCumulativeNormal.png|Graphs of Beta distribution cumulative functions with borders 0 and 1]] | ||
+ | |} | ||
+ | |||
+ | {| | ||
+ | |<tt>'''BETADIST(1.1;1;0.5;0;1;TRUE())</tt> | ||
+ | : returns 1 | ||
+ | before version 3.1: <tt>'''BETADIST(1.1;1;0.5;0;1)</tt> | ||
+ | : returns ''Invalid argument'' | ||
+ | |[[Image:BetaDistributionCumulativeSpecial.png|Graphs of Beta distribution cumulative functions with alpha=1]] | ||
+ | |} | ||
− | + | {{SeeAlso|EN| | |
− | [[Documentation/How_Tos/Calc: BETAINV function| | + | * [[Documentation/How_Tos/Calc: BETAINV function|BETAINV]] |
− | [[Documentation/How_Tos/Calc: Statistical functions| | + | * [[Documentation/How_Tos/Calc: Statistical functions|Statistical functions]] |
− | [[Documentation/How_Tos/Calc: Functions listed alphabetically| | + | * [[Documentation/How_Tos/Calc: Functions listed alphabetically|Functions listed alphabetically]] |
− | [[Documentation/How_Tos/Calc: Functions listed by category| | + | * [[Documentation/How_Tos/Calc: Functions listed by category|Functions listed by category]] |
+ | }} | ||
+ | [[Category: Documentation/Reference/Calc/Statistical functions]] |