lmomco (version 0.6)

pwm2lmom: Probability-Weighted Moments to L-moments

Description

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.

$${\lambda }_1={\beta }_0\text{,}$$ $${\lambda }_2=2{\beta }_1-{\beta }_0\text{,}$$ $${\lambda }_3=6{\beta }_2-6{\beta }_1+{\beta }_0\text{,}$$ $${\lambda }_4=20{\beta }_3-30{\beta }_2+12{\beta }_1-{\beta }_0\text{,}$$ $${\lambda }_5=70{\beta }_4-140{\beta }_3+90{\beta }_2-20{\beta }_1+{\beta }_0\text{,}$$ $$\tau ={\lambda }_2/{\lambda }_1\text{,}$$ $${\tau }_3={\lambda }_3/{\lambda }_2\text{,}$$ $${\tau }_4={\lambda }_4/{\lambda }_2\text{, and}$$ $${\tau }_5={\lambda }_5/{\lambda }_2\text{.}$$

Usage

pwm2lmom(pwm)

Arguments

pwm

A PWM object created by pwm.ub or similar.

Value

• 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

Details

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.

References

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.

See Also

lmom.ub, pwm.ub, lmom2pwm

Examples

lmom <- pwm2lmom(pwm.ub(c(123,34,4,654,37,78)))

pwm2lmom(pwm.ub(rnorm(100)))