# parkur: Estimate the Parameters of the Kumaraswamy Distribution

### Description

This function estimates the parameters of the Kumaraswamy distribution given the L-moments of the data in an L-moment object such as that returned by `lmoms`. The relations between distribution parameters and L-moments are seen under `lmomkur`.

### Usage

 `1` ```parkur(lmom, checklmom=TRUE, ...) ```

### Arguments

 `lmom` An L-moment object created by `lmoms` or `vec2lmom`. `checklmom` Should the `lmom` be checked for validity using the `are.lmom.valid` function. Normally this should be left as the default and it is very unlikely that the L-moments will not be viable (particularly in the τ_4 and τ_3 inequality). However, for some circumstances or large simulation exercises then one might want to bypass this check. `...` Other arguments to pass.

### Value

An R `list` is returned.

 `type` The type of distribution: `kur`. `para` The parameters of the distribution. `err` The convergence error. `convergence` Logical showing whether error convergence occurred. `source` The source of the parameters: “parkur”.

W.H. Asquith

### References

Jones, M.C., 2009, Kumaraswamy's distribution—A beta-type distribution with some tractability advantages: Statistical Methodology, v. 6, pp. 70–81.

`lmomkur`, `cdfkur`, `pdfkur`, `quakur`

### Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18``` ```lmr <- lmoms(runif(20)^2) parkur(lmr) kurpar <- list(para=c(1,1), type="kur"); lmr <- lmomkur(kurpar) parkur(lmr) kurpar <- list(para=c(0.1,1), type="kur"); lmr <- lmomkur(kurpar) parkur(lmr) kurpar <- list(para=c(1,0.1), type="kur"); lmr <- lmomkur(kurpar) parkur(lmr) kurpar <- list(para=c(0.1,0.1), type="kur"); lmr <- lmomkur(kurpar) parkur(lmr) ```

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