Kumaraswamy distribution maximum likelihood estimation

Uses Newton-Raphson to estimate the parameters of the Kumaraswamy distribution.

mlkumar(x, na.rm = FALSE, a0 = 1, rel.tol = .Machine$double.eps^0.25,
  iterlim = 100)

Arguments

x	a (non-empty) numeric vector of data values.
na.rm	logical. Should missing values be removed?
a0	An optional starting value for the `a` parameter.
rel.tol	Relative accuracy requested.
iterlim	A positive integer specifying the maximum number of iterations to be performed before the program is terminated.

Value

mlkumar returns an object of class univariateML. This is a named numeric vector with maximum likelihood estimates for a and b and the following attributes:

model

The name of the model.

density

The density associated with the estimates.

logLik

The loglikelihood at the maximum.

support

The support of the density.

n

The number of observations.

call

The call as captured my match.call

Details

For the density function of the Kumaraswamy distribution see Kumaraswamy.

References

Jones, M. C. "Kumaraswamy's distribution: A beta-type distribution with some tractability advantages." Statistical Methodology 6.1 (2009): 70-81.

Kumaraswamy, Ponnambalam. "A generalized probability density function for double-bounded random processes." Journal of Hydrology 46.1-2 (1980): 79-88.

Examples

AIC(mlkumar(USArrests$Rape / 100))
#> [1] -96.06926