# pel-functions: Parameter estimation for specific distributions by the method... In lmom: L-Moments

 pel-functions R Documentation

## Parameter estimation for specific distributions by the method of L-moments

### Description

Computes the parameters of a probability distribution as a function of the L-moments. The following distributions are recognized:

 pelexp exponential pelgam gamma pelgev generalized extreme-value pelglo generalized logistic pelgpa generalized Pareto pelgno generalized normal pelgum Gumbel (extreme-value type I) pelkap kappa pelln3 three-parameter lognormal pelnor normal pelpe3 Pearson type III pelwak Wakeby pelwei Weibull

### Usage

pelexp(lmom)
pelgam(lmom)
pelgev(lmom)
pelglo(lmom)
pelgno(lmom)
pelgpa(lmom, bound = NULL)
pelgum(lmom)
pelkap(lmom)
pelln3(lmom, bound = NULL)
pelnor(lmom)
pelpe3(lmom)
pelwak(lmom, bound = NULL, verbose = FALSE)
pelwei(lmom, bound = NULL)


### Arguments

 lmom Numeric vector containing the L-moments of the distribution or of a data sample. bound Lower bound of the distribution. If NULL (the default), the lower bound will be estimated along with the other parameters. verbose Logical: whether to print a message when not all parameters of the distribution can be computed.

### Details

Numerical methods and accuracy are as described in Hosking (1996, pp. 10–11). Exception: if pelwak is unable to fit a Wakeby distribution using all 5 L-moments, it instead fits a generalized Pareto distribution to the first 3 L-moments. (The corresponding routine in the LMOMENTS Fortran package would attempt to fit a Wakeby distribution with lower bound zero.)

The kappa and Wakeby distributions have 4 and 5 parameters respectively but cannot attain all possible values of the first 4 or 5 L-moments. Function pelkap can fit only kappa distributions with \tau_4 <= (1 + 5 \tau_3^2) / 6 (the limit is the (\tau_3, \tau_4) relation satisfied by the generalized logistic distribution), and will give an error if lmom does not satisfy this constraint. Function pelwak can fit a Wakeby distribution only if the (\tau_3,\tau_4) values lie above a line plotted by lmrd(distributions="WAK.LB"), and if \tau_5 satisfies additional constraints; in other cases pelwak will fit a generalized Pareto distribution (a special case of the Wakeby distribution) to the first three L-moments.

### Value

A numeric vector containing the parameters of the distribution.

### Author(s)

J. R. M. Hosking jrmhosking@gmail.com

### References

Hosking, J. R. M. (1996). Fortran routines for use with the method of L-moments, Version 3. Research Report RC20525, IBM Research Division, Yorktown Heights, N.Y.

pelp for parameter estimation of a general distribution specified by its cumulative distribution function or quantile function.

lmrexp, etc., to compute the L-moments of a distribution given its parameters.

For individual distributions, see their cumulative distribution functions:

 cdfexp exponential cdfgam gamma cdfgev generalized extreme-value cdfglo generalized logistic cdfgpa generalized Pareto cdfgno generalized normal cdfgum Gumbel (extreme-value type I) cdfkap kappa cdfln3 three-parameter lognormal cdfnor normal cdfpe3 Pearson type III cdfwak Wakeby cdfwei Weibull

### Examples

# Sample L-moments of Ozone from the airquality data
data(airquality)
lmom <- samlmu(airquality\$Ozone)

# Fit a GEV distribution
pelgev(lmom)


lmom documentation built on Aug. 29, 2023, 9:07 a.m.