kumar {VGAM} | R Documentation

## 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`.

### Details

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.

### Value

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

### Author(s)

T. W. Yee

### 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)

[Package VGAM version 0.7-9 Index]