pwm2lmom {lmomco} | R Documentation |
Converts the Probability-Weighted Moments (PWM) to the L-moments given the PWM. The conversion is linear so procedures based on PWMs and identical to those based on L-moments.
λ_1 = β_0 mbox{,}
λ_2 = 2β_1 - β_0 mbox{,}
λ_3 = 6β_2 - 6β_1 + β_0 mbox{,}
λ_4 = 20β_3 - 30β_2 + 12β_1 - β_0 mbox{,}
λ_5 = 70β_4 - 140β_3 + 90β_2 - 20β_1 + β_0 mbox{,}
tau = λ_2/λ_1 mbox{,}
tau_3 = λ_3/λ_2 mbox{,}
tau_4 = λ_4/λ_2 mbox{, and}
tau_5 = λ_5/λ_2 mbox{.}
pwm2lmom(pwm)
pwm |
A PWM object created by pwm.ub or similar. |
The Probability Weighted Moments (PWMs) are linear combinations of the L-moments and therefore contain the same statistical information of the data as the L-moments. However, the PWMs are harder to interpret as measures of probability distributions. The linearity between L-moments and Probability-Weighted Moments means that procedures base on one are equivalent to the other.
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 |
W.H. Asquith
Greenwood, J.A., Landwehr, J.M., Matalas, N.C., and Wallis, J.R., 1979, Probability weighted moments—Definition and relation to parameters of several distributions expressable in inverse form: Water Resources Research, vol. 15, p. 1,049–1,054.
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.
lmom <- pwm2lmom(pwm.ub(c(123,34,4,654,37,78))) pwm2lmom(pwm.ub(rnorm(100)))