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lmom

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)

Arguments

para

Numeric vector containing the parameters of the distribution.
nmom

The number of L-moments to be calculated.

Details

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

Value

Numeric vector containing the L-moments.

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.

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)
lmom

L-Moments

v2.8
Common Public License Version 1.0
Authors
J. R. M. Hosking
Initial release
2019-03-11

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