lmom (version 3.2)

pel-functions: 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)

Value

A numeric vector containing the parameters of the distribution.

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.

Author

J. R. M. Hosking

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 \(\tau_4 \le (1 + 5 \tau_3^2) / 6\) (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, when plotted on an \(L\)-moment ratio diagram, 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.

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.

See Also

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)