kumar {VGAM} | R Documentation |
Estimates the two parameters of the Kumaraswamy distribution by maximum likelihood estimation.
kumar(lshape1="loge", lshape2="loge", eshape1=list(), eshape2=list(), ishape1=NULL, ishape2=NULL, nsimEIM=500, zero=NULL)
lshape1, lshape2 |
Link function for the two positive shape parameters.
See Links for more choices.
|
eshape1, eshape2 |
List. Extra argument for each of the links.
See earg in Links for general information.
|
ishape1, ishape2 |
Numeric.
Optional initial values for the two positive shape parameters.
|
nsimEIM, zero |
See CommonVGAMffArguments .
|
The Kumaraswamy distribution has density function
a*b*y^(a-1)*(1-y^a)^(b-1)
where 0 < y < 1 and the two shape parameters, a and b, are positive. The mean is b Beta(1+1/a,b) (returned as the fitted values) and the variance is b Beta(1+2/a,b) - (b Beta(1+1/a,b))^2. Applications of the Kumaraswamy distribution include the storage volume of a water reservoir.
An object of class "vglmff"
(see vglmff-class
).
The object is used by modelling functions such as vglm
and vgam
.
T. W. Yee
Kumaraswamy, P. (1980). A generalized probability density function for double-bounded random processes. Journal of Hydrology, 46, 79–88.
shape1 = exp(1); shape2 = exp(2); y = rkumar(n <- 1000, shape1, shape2) fit = vglm(y ~ 1, kumar, trace =TRUE) c(mean(y), fitted(fit)[1]) coef(fit, matrix=TRUE) Coef(fit) summary(fit)