# pargpa: Estimate the Parameters of the Generalized Pareto... In lmomco: L-Moments, Censored L-Moments, Trimmed L-Moments, L-Comoments, and Many Distributions

 pargpa R Documentation

## Estimate the Parameters of the Generalized Pareto Distribution

### Description

This function estimates the parameters of the Generalized Pareto distribution given the L-moments of the data in an ordinary L-moment object (`lmoms`) or a trimmed L-moment object (`TLmoms` for `t=1`). The relations between distribution parameters and L-moments are seen under `lmomgpa` or `lmomTLgpa`.

### Usage

```pargpa(lmom, zeta=1, xi=NULL, checklmom=TRUE, ...)
```

### Arguments

 `lmom` An L-moment object created by `lmoms`, `TLmoms` with `trim=0`, or `vec2lmom`. `zeta` The right censoring fraction. If less than unity then a dispatch to the `pargpaRC` is made and the `lmom` argument must contain the B-type L-moments. If the data are not right censored, then this value must be left alone to the default of unity. `xi` The lower limit of the distribution. If ξ is known, then alternative algorithms are used. `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: `gpa`. `para` The parameters of the distribution. `source` The source of the parameters: “pargpa”.

W.H. Asquith

### References

Hosking, J.R.M., 1990, L-moments—Analysis and estimation of distributions using linear combinations of order statistics: Journal of the Royal Statistical Society, Series B, v. 52, pp. 105–124.

Hosking, J.R.M., 1996, FORTRAN routines for use with the method of L-moments: Version 3, IBM Research Report RC20525, T.J. Watson Research Center, Yorktown Heights, New York.

Hosking, J.R.M., and Wallis, J.R., 1997, Regional frequency analysis—An approach based on L-moments: Cambridge University Press.

`lmomgpa`, `cdfgpa`, `pdfgpa`, `quagpa`

### Examples

```X   <- rexp(200)
lmr <- lmoms(X)
P1  <- pargpa(lmr)
P2  <- pargpa(lmr, xi=0.25)

## Not run:
F <- nonexceeds()
plot(pp(X), sort(X))
lines(F,quagpa(F,P1))  # black line
lines(F, quagpa(F,P2), col=2)   # red line

## End(Not run)
```

lmomco documentation built on Aug. 27, 2022, 1:06 a.m.