lmom.ub {lmomco} | R Documentation |
Unbiased sample L-moments are computed for a vector using the direct sample estimation
method as opposed to the use of sample probability-weighted moments. The L-moments are the ordinary L-moments and not the trimmed L-moments (see
TLmoms
). The mean,
L-scale, coefficient of L-variation (tau, LCV, L-scale/mean),
L-skew (tau_3, TAU3, L3/L2),
L-kurtosis (tau_4, TAU4, L4/L2), and tau_5 (TAU5, L4/L2) are computed.
In conventional nomenclature, the L-moments are
hat{λ}_1 = mbox{L1} = mbox{mean, }
hat{λ}_2 = mbox{L2} = mbox{L-scale, }
hat{λ}_3 = mbox{L3} = mbox{third L-moment, }
hat{λ}_4 = mbox{L4} = mbox{fourth L-moment, }
hat{λ}_5 = mbox{L5} = mbox{fifth L-moment, }
hat{tau} = mbox{LCV} = λ_2/λ_1 = mbox{coefficient of L-variation, }
hat{tau}_3 = mbox{TAU3} = λ_3/λ_2 = mbox{L-skew, }
hat{tau}_4 = mbox{TAU4} = λ_4/λ_2 = mbox{L-kurtosis, and}
hat{tau}_5 = mbox{TAU5} = λ_5/λ_2 = mbox{not named.}
lmom.ub(x)
x |
A vector of data values. |
The L-moment ratios (tau, tau_3, tau_4, and tau_5)
are the primary higher L-moments for application, such as for distribution parameter estimation.
However, the actual L-moments (λ_3, λ_4, and λ_5) are also
reported. This implementation of L-moment calculation requires a minimum of five data points. If you want to compute more or fewer L-moments, then see lmoms
.
An R list
is returned.
L1 |
Arithmetic mean. |
L2 |
L-scale—analogous to standard deviation. |
LCV |
coefficient of L-variation—analogous to coe. of variation. |
TAU3 |
The third L-moment ratio or L-skew—analogous to skew. |
TAU4 |
The fourth L-moment ratio or L-kurtosis—analogous to kurtosis. |
TAU5 |
The fifth L-moment ratio. |
L3 |
The third L-moment. |
L4 |
The fourth L-moment. |
L5 |
The fifth L-moment. |
source |
An attribute identifying the computational source of the L-moments: “lmom.ub”. |
W.H. Asquith
The Perl code base of W.H. Asquith
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, vol. 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.
Wang, Q.J., 1996b, Direct sample estimators of L-moments: Water Resources Research, vol. 32, no. 12., pp. 3617–3619.
lmom2pwm
, pwm.ub
, pwm2lmom
, lmoms
, and lmorph
lmr <- lmom.ub(c(123,34,4,654,37,78)) lmorph(lmr) lmom.ub(rnorm(100))