Difference between revisions of "Documentation/How Tos/Calc: BETADIST function"
Line 48: | Line 48: | ||
=== 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> | + | {| |
+ | |<tt>'''BETADIST(1;1;0.5;0;1;FALSE())</tt> | ||
: returns ''illegal argument'' because there is a pole | : returns ''illegal 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()</tt> | ||
+ | |[[Image:BetaDistributionCumulativeLocationScale.png|Graphs of Beta distribution cumulative functions using parameter a and b]] | ||
+ | |} | ||
+ | |||
+ | {| | ||
+ | |<tt>'''BETADIST()</tt> | ||
+ | |[[Image:BetaDistributionCumulativeNormal.png|Graphs of Beta distribution cumulative functions with borders 0 and 1]] | ||
+ | |} | ||
+ | |||
+ | {| | ||
+ | |<tt>'''BETADIST()</tt> | ||
+ | |[[Image:BetaDistributionCumulativeSpecial.png|Graphs of Beta distribution cumulative functions with alpha=1]] | ||
+ | |} | ||
=== See also === | === See also === |
Revision as of 19:43, 6 December 2008
BETADIST
Calculates the cumulative distribution function or the probability density function of a beta distribution.
Syntax
BETADIST(x; α; β; a; b; cumulative)
The beta distribution is a family of continuous probability distributions, where α and β are parameters controlling the shape of the distribution.
The parameters a and b are lower and upper bounds of the distribution. You can interpret the value a as location and the value b−a as scale.
a and b are optional parameters which default (if omitted) to 0 and 1.
cumulative is an optional 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.
Constraints:
- α > 0 , β > 0 , a < b
- If α < 1, than the density function has a pole at x = a.
- If β < 1, than the density function has a pole at x = b.
Semantic
For cumulative = FALSE() the function BETADIST calculates the probability density function (besides the constraints given above):
For cumulative = TRUE() the function BETADIST calculates the cumulative distribution function:
Notice, that
where
and is the regularized incomplete Beta function.
Example
BETADIST(1;5;3;-2;4;FALSE())
|
BETADIST(0.2;0.7;4;0;1;FALSE())
|
BETADIST(1;1;0.5;0;1;FALSE())
BETADIST(1.1;1;0.5;0;1;FALSE())
|
BETADIST() |
BETADIST() |
BETADIST() |
See also
Functions listed alphabetically, Functions listed by category