VGAM (version 0.7-5)

kumar: Kumaraswamy Distribution Family Function

Description

Estimates the two parameters of the Kumaraswamy distribution by maximum likelihood estimation.

Usage

kumar(lshape1="loge", lshape2="loge",
      eshape1=list(), eshape2=list(),
      ishape1=NULL, ishape2=NULL, nsimEIM=500, zero=NULL)

Arguments

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.

Value

• An object of class "vglmff" (see vglmff-class). The object is used by modelling functions such as vglm and vgam.

Details

The Kumaraswamy distribution distribution has density function $$f(y;a=shape1,b=shape2) = a b y^{a-1} (1-y^{a})^{b-1}$$ 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.

References

Kumaraswamy, P. (1980). A generalized probability density function for double-bounded random processes. Journal of Hydrology, 46, 79--88.

See Also

dkumar, betaff.

Examples

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)