lmomco (version 2.3.1)

lmomgam: L-moments of the Gamma Distribution

Description

This function estimates the L-moments of the Gamma distribution given the parameters (\(\alpha\) and \(\beta\)) from pargam. The L-moments in terms of the parameters are complicated and solved numerically. This function is adaptive to the 2-parameter and 3-parameter Gamma versions supported by this package. For legacy reasons, lmomco continues to use a port of Hosking's FORTRAN into R if the 2-parameter distribution is used but the 3-parameter generalized Gamma distribution calls upon theoLmoms.max.ostat. Alternatively, the theoTLmoms could be used: theoTLmoms(para) is conceptually equivalent to the internal calls to theoLmoms.max.ostat made for the lmomgam implementation.

Usage

lmomgam(para, ...)

Arguments

para

The parameters of the distribution.

...

Additional arguments to pass to theoLmoms.max.ostat.

Value

An R list is returned.

lambdas

Vector of the L-moments. First element is \(\lambda_1\), second element is \(\lambda_2\), and so on.

ratios

Vector of the L-moment ratios. Second element is \(\tau\), third element is \(\tau_3\) and so on.

trim

Level of symmetrical trimming used in the computation, which is 0.

leftrim

Level of left-tail trimming used in the computation, which is NULL.

rightrim

Level of right-tail trimming used in the computation, which is NULL.

source

An attribute identifying the computational source of the L-moments: “lmomgam”.

References

Hosking, J.R.M., 1990, L-moments---Analysis and estimation of distributions using linear combinations of order statistics: Journal of the Royal Statistical Society, Series B, v. 52, p. 105--124.

Hosking, J.R.M., 1996, FORTRAN routines for use with the method of L-moments: Version 3, IBM Research Report RC20525, T.J. Watson Research Center, Yorktown Heights, New York.

Hosking, J.R.M., and Wallis, J.R., 1997, Regional frequency analysis---An approach based on L-moments: Cambridge University Press.

See Also

pargam, cdfgam, pdfgam, quagam

Examples

# NOT RUN {
lmomgam(pargam(lmoms(c(123,34,4,654,37,78))))

# }
# NOT RUN {
# 3-p Generalized Gamma Distribution and comparisons of 3-p Gam parameterization.
#     1st parameter A[lmomco] = A[gamlss] =  exp(A[flexsurv])
#     2nd parameter B[lmomco] = B[gamlss] =      B[flexsurv]
#     3rd parameter C[lmomco] = C[gamlss] -->    C[flexsurv] = B[lmomco]/C[lmomco]
lmomgam(vec2par(c(7.4, 0.2, 14), type="gam"), nmom=5)$lambdas      # numerics
lmoms(gamlss.dist::rGG(50000, mu=7.4, sigma=0.2, nu=14))$lambdas   # simulation
lmoms(flexsurv::rgengamma(50000, log(7.4), 0.2, Q=0.2*14))$lambdas # simulation
#[1]  5.364557537  1.207492689 -0.110129217  0.067007941 -0.006747895
#[1]  5.366707749  1.209455502 -0.108354729  0.066360223 -0.006716783
#[1]  5.356166684  1.197942329 -0.106745364  0.069102821 -0.008293398#
# }