lmom (version 3.2)

lmr-functions: L-moments of specific probability distributions

Description

Computes the \(L\)-moments of a probability distribution given its parameters. The following distributions are recognized:

	lmrexp	exponential
	lmrgam	gamma
	lmrgev	generalized extreme-value
	lmrglo	generalized logistic
	lmrgpa	generalized Pareto
	lmrgno	generalized normal
	lmrgum	Gumbel (extreme-value type I)
	lmrkap	kappa
	lmrln3	three-parameter lognormal
	lmrnor	normal
	lmrpe3	Pearson type III
	lmrwak	Wakeby
	lmrwei	Weibull

Usage

lmrexp(para = c(0, 1), nmom = 2)
lmrgam(para = c(1, 1), nmom = 2)
lmrgev(para = c(0, 1, 0), nmom = 3)
lmrglo(para = c(0, 1, 0), nmom = 3)
lmrgno(para = c(0, 1, 0), nmom = 3)
lmrgpa(para = c(0, 1, 0), nmom = 3)
lmrgum(para = c(0, 1), nmom = 2)
lmrkap(para = c(0, 1, 0, 0), nmom = 4)
lmrln3(para = c(0, 0, 1), nmom = 3)
lmrnor(para = c(0, 1), nmom = 2)
lmrpe3(para = c(0, 1, 0), nmom = 3)
lmrwak(para = c(0, 1, 0, 0, 0), nmom = 5)
lmrwei(para = c(0, 1, 1), nmom = 3)

Value

Numeric vector containing the \(L\)-moments.

Arguments

para

Numeric vector containing the parameters of the distribution.

nmom

The number of \(L\)-moments to be calculated.

Author

J. R. M. Hosking

Details

Numerical methods and accuracy are as described in Hosking (1996, pp. 8--9).

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

lmrp to compute \(L\)-moments of a general distribution specified by its cumulative distribution function or quantile function.

samlmu to compute \(L\)-moments of a data sample.

pelexp, etc., to compute the parameters of a distribution given its \(L\)-moments.

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

# Compare sample L-moments of Ozone from the airquality data
# with the L-moments of a GEV distribution fitted to the data
data(airquality)
smom <- samlmu(airquality$Ozone, nmom=6)
gevpar <- pelgev(smom)
pmom <- lmrgev(gevpar, nmom=6)
print(smom)
print(pmom)