L-moments of specific probability distributions

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

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.

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.

Author

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

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)
#>         l_1         l_2         t_3         t_4         t_5         t_6 
#> 42.12931034 17.63845577  0.28394953  0.10661829  0.03222640  0.03781762 
print(pmom)
#>    lambda_1    lambda_2       tau_3       tau_4       tau_5       tau_6 
#> 42.12931034 17.63845577  0.28394956  0.20554284  0.11152060  0.09341537

	`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