Betadf: Difference between revisions
Jump to navigation
Jump to search
imported>Jeremy (Importing text file) |
imported>Jeremy (Importing text file) |
||
| Line 1: | Line 1: | ||
===Purpose=== | ===Purpose=== | ||
Beta distribution. | Beta distribution. | ||
===Synopsis=== | ===Synopsis=== | ||
:prob = betadf(function,x,a,b,''options'') | :prob = betadf(function,x,a,b,''options'') | ||
===Description=== | ===Description=== | ||
Estimates cumulative distribution function (cumulative, cdf), probability density function (density, pdf), quantile (inverse of cdf), or random numbers for a Beta distribution. | Estimates cumulative distribution function (cumulative, cdf), probability density function (density, pdf), quantile (inverse of cdf), or random numbers for a Beta distribution. | ||
This distribution is commonly used to model activity time. In its usual form, the data must be in (0,1), but this toolbox will allow both a location and scale parameter (in addition to the a and b above). This may be symmetric or asymmetric. | This distribution is commonly used to model activity time. In its usual form, the data must be in (0,1), but this toolbox will allow both a location and scale parameter (in addition to the a and b above). This may be symmetric or asymmetric. | ||
====INPUTS==== | ====INPUTS==== | ||
* '''function''' = [ {'cumulative'} | 'density' | 'quantile' | 'random' ], defines the functionality to be used. Note that the function recognizes the first letter of each string so that the string could be: [ 'c' | 'd' | 'q' | 'r' ]. | * '''function''' = [ {'cumulative'} | 'density' | 'quantile' | 'random' ], defines the functionality to be used. Note that the function recognizes the first letter of each string so that the string could be: [ 'c' | 'd' | 'q' | 'r' ]. | ||
* '''x''' = matrix in which the sample data is stored, in the interval (0,1). | * '''x''' = matrix in which the sample data is stored, in the interval (0,1). | ||
* '''for''' function=quantile - matrix with values in the interval (0,1). | * '''for''' function=quantile - matrix with values in the interval (0,1). | ||
* '''for''' function=random - vector indicating the size of the random matrix to create. | * '''for''' function=random - vector indicating the size of the random matrix to create. | ||
* '''a''' = scale parameter (real and nonnegative). | * '''a''' = scale parameter (real and nonnegative). | ||
* '''b''' = shape parameter (real and nonnegative). | * '''b''' = shape parameter (real and nonnegative). | ||
'''Note''': If inputs (x, a, and b) are not equal in size, the function will attempt to resize all inputs to the largest input using the RESIZE function. | '''Note''': If inputs (x, a, and b) are not equal in size, the function will attempt to resize all inputs to the largest input using the RESIZE function. | ||
'''Note''': Functions will typically allow input values outside of the acceptable range to be passed but such values will return NaN in the results. | '''Note''': Functions will typically allow input values outside of the acceptable range to be passed but such values will return NaN in the results. | ||
===Options=== | ===Options=== | ||
''options'' is a structure array with the following fields: | ''options'' is a structure array with the following fields: | ||
* '''name''': 'options', name indicating that this is an options structure, | * '''name''': 'options', name indicating that this is an options structure, | ||
* '''scale''': {1}, scale for the ordinate, and | * '''scale''': {1}, scale for the ordinate, and | ||
* '''offset''': {0}, offset for the ordinate. | * '''offset''': {0}, offset for the ordinate. | ||
The default options structure can be retrieved using: options = betadf('options'). | The default options structure can be retrieved using: options = betadf('options'). | ||
===Examples=== | ===Examples=== | ||
===Cumulative''':===''' | ===Cumulative''':===''' | ||
>> prob = betadf('c', [0.85 0.9],1,2) | >> prob = betadf('c', [0.85 0.9],1,2) | ||
prob = | prob = | ||
## 0.9900 | ## 0.9900 | ||
>> x = [0:0.01:1]; | >> x = [0:0.01:1]; | ||
>> plot(x,betadf('c',x,1,2),'b-',x,betadf('c',x,0.5,0.5),'r-') | >> plot(x,betadf('c',x,1,2),'b-',x,betadf('c',x,0.5,0.5),'r-') | ||
====Density:==== | ====Density:==== | ||
>> prob = betadf('d', 0.9, 1, 2) | >> prob = betadf('d', 0.9, 1, 2) | ||
prob = | prob = | ||
0.2000 | 0.2000 | ||
>> x = [0:0.01:1]; | >> x = [0:0.01:1]; | ||
>> plot(x,betadf('d',x,1,2),'b-',x,betadf('d',x,0.5,0.5),'r-') | >> plot(x,betadf('d',x,1,2),'b-',x,betadf('d',x,0.5,0.5),'r-') | ||
====Quantile:==== | ====Quantile:==== | ||
>> prob = betadf('q',[0.9775 0.9900]',1,2) | >> prob = betadf('q',[0.9775 0.9900]',1,2) | ||
prob = | prob = | ||
0.8500 | 0.8500 | ||
0.9000 | 0.9000 | ||
====Random:==== | ====Random:==== | ||
>> prob = betadf('r',[5 1],1,2) | >> prob = betadf('r',[5 1],1,2) | ||
prob = | prob = | ||
0.3791 | 0.3791 | ||
0.2549 | 0.2549 | ||
0.8169 | 0.8169 | ||
0.0216 | 0.0216 | ||
0.1516 | 0.1516 | ||
===See Also=== | ===See Also=== | ||
[[betadr]], [[cauchydf]], [[chidf]], [[expdf]], [[gammadf]], [[gumbeldf]], [[laplacedf]], [[logisdf]], [[lognormdf]], [[normdf]], [[paretodf]], [[raydf]], [[triangledf]], [[unifdf]], [[weibulldf]] | [[betadr]], [[cauchydf]], [[chidf]], [[expdf]], [[gammadf]], [[gumbeldf]], [[laplacedf]], [[logisdf]], [[lognormdf]], [[normdf]], [[paretodf]], [[raydf]], [[triangledf]], [[unifdf]], [[weibulldf]] | ||
Revision as of 14:24, 3 September 2008
Purpose
Beta distribution.
Synopsis
- prob = betadf(function,x,a,b,options)
Description
Estimates cumulative distribution function (cumulative, cdf), probability density function (density, pdf), quantile (inverse of cdf), or random numbers for a Beta distribution.
This distribution is commonly used to model activity time. In its usual form, the data must be in (0,1), but this toolbox will allow both a location and scale parameter (in addition to the a and b above). This may be symmetric or asymmetric.
INPUTS
- function = [ {'cumulative'} | 'density' | 'quantile' | 'random' ], defines the functionality to be used. Note that the function recognizes the first letter of each string so that the string could be: [ 'c' | 'd' | 'q' | 'r' ].
- x = matrix in which the sample data is stored, in the interval (0,1).
- for function=quantile - matrix with values in the interval (0,1).
- for function=random - vector indicating the size of the random matrix to create.
- a = scale parameter (real and nonnegative).
- b = shape parameter (real and nonnegative).
Note: If inputs (x, a, and b) are not equal in size, the function will attempt to resize all inputs to the largest input using the RESIZE function.
Note: Functions will typically allow input values outside of the acceptable range to be passed but such values will return NaN in the results.
Options
options is a structure array with the following fields:
- name: 'options', name indicating that this is an options structure,
- scale: {1}, scale for the ordinate, and
- offset: {0}, offset for the ordinate.
The default options structure can be retrieved using: options = betadf('options').
Examples
===Cumulative:===
>> prob = betadf('c', [0.85 0.9],1,2)
prob =
- 0.9900
>> x = [0:0.01:1];
>> plot(x,betadf('c',x,1,2),'b-',x,betadf('c',x,0.5,0.5),'r-')
Density:
>> prob = betadf('d', 0.9, 1, 2)
prob =
0.2000
>> x = [0:0.01:1];
>> plot(x,betadf('d',x,1,2),'b-',x,betadf('d',x,0.5,0.5),'r-')
Quantile:
>> prob = betadf('q',[0.9775 0.9900]',1,2)
prob =
0.8500
0.9000
Random:
>> prob = betadf('r',[5 1],1,2)
prob =
0.3791
0.2549
0.8169
0.0216
0.1516
See Also
betadr, cauchydf, chidf, expdf, gammadf, gumbeldf, laplacedf, logisdf, lognormdf, normdf, paretodf, raydf, triangledf, unifdf, weibulldf