Gumbeldf: Difference between revisions
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This distribution is also known as the Type I extreme value distribution. It is an alternative to the Weibull distribution. | This distribution is also known as the Type I extreme value distribution. It is an alternative to the Weibull distribution. | ||
::<math>f(x) = \frac { \Gamma \left [ \frac {a+b} {2} \right ] \left ( a/b \right )^{a/2} x^{\left ( a-2 \right ) /2}} {\Gamma \left ( \frac {a} {2} \right ) \Gamma \left ( \frac {b} {2} \right ) \left [ 1+ \frac {a} {b} x \right ] ^{\left ( a+b \right )/2}}</math> | |||
====Inputs==== | ====Inputs==== | ||
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'''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. | ||
===Examples=== | ===Examples=== | ||
Latest revision as of 06:15, 10 October 2008
Purpose
Gumbel distribution.
Synopsis
- prob = gumbeldf(function,x,a,b)
Description
Estimates cumulative distribution function (cumulative, cdf), probability density function (density, pdf), quantile (inverse of cdf), or random numbers for a Gumbel distribution.
This distribution is also known as the Type I extreme value distribution. It is an alternative to the Weibull distribution.
![{\displaystyle f(x)={\frac {\Gamma \left[{\frac {a+b}{2}}\right]\left(a/b\right)^{a/2}x^{\left(a-2\right)/2}}{\Gamma \left({\frac {a}{2}}\right)\Gamma \left({\frac {b}{2}}\right)\left[1+{\frac {a}{b}}x\right]^{\left(a+b\right)/2}}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/c2176192ed793db56f6640039f8d3691b03e028c)
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 (-inf,inf).
- 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 = mode/location parameter (real).
- b = scale parameter (real and positive).
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.
Examples
Cumulative
>> prob = gumbeldf('c',0.99,0.5,1)
prob =
0.5419
>> x = [0:0.1:10];
>> plot(x,gumbeldf('c',x,2),'b-',x,gumbeldf('c',x,0.5),'r-')
Density
>> prob = gumbeldf('d',0.99,0.5,1)
prob =
0.3320
>> x = [0:0.1:10];
>> plot(x,gumbeldf('d',x,2),'b-',x,gumbeldf('d',x,0.5),'r-')
Quantile
>> prob = gumbeldf('q',0.99,0.5,1)
prob =
5.1001
Random
>> prob = gumbeldf('r',[4 1],2,1)
ans =
3.8437
2.6508
2.3566
4.2479
See Also
betadf, cauchydf, chidf, expdf, gammadf, laplacedf, logisdf, lognormdf, normdf, paretodf, raydf, triangledf, unifdf, weibulldf