# mlkumar: Kumaraswamy distribution maximum likelihood estimation In univariateML: Maximum Likelihood Estimation for Univariate Densities

## Description

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

## Usage

 `1` ```mlkumar(x, na.rm = FALSE, ...) ```

## Arguments

 `x` a (non-empty) numeric vector of data values. `na.rm` logical. Should missing values be removed? `...` `a0` is an optional starting value for the `a` parameter. `rel.tol` is the relative accuracy requested, defaults to `.Machine\$double.eps^0.25`. `iterlim` is a positive integer specifying the maximum number of iterations to be performed before the program is terminated (defaults to `100`).

## Details

For the density function of the Kumaraswamy distribution see Kumaraswamy.

## 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`

## 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.

Kumaraswamy for the Kumaraswamy density.

## Examples

 `1` ```AIC(mlkumar(USArrests\$Rape / 100)) ```

### Example output

```[1] -96.06926
```

univariateML documentation built on Aug. 6, 2020, 1:11 a.m.