pwm2lmom: Probability-Weighted Moments to L-moments

Description Usage Arguments Details Value Author(s) References See Also Examples

Description

Converts the probability-weighted moments (PWM) to the L-moments. The conversion is linear so procedures based on PWMs are identical to those based on L-moments through a system of linear equations

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{,}

τ = λ_2/λ_1 \mbox{,}

τ_3 = λ_3/λ_2 \mbox{,}

τ_4 = λ_4/λ_2 \mbox{, and}

τ_5 = λ_5/λ_2 \mbox{.}

The general expression and the expression used for computation if the argument is a vector of PWMs is

λ_{r+1} = ∑^r_{k=0} (-1)^{r-k}{r \choose k}{r+k \choose k} β_{k+1}\mbox{.}

Usage

1

Arguments

pwm

A PWM object created by pwm.ub or similar.

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 PWMs means that procedures base on one are equivalent to the other.

The function can take a variety of PWM argument types in pwm. The function checks whether the argument is an R list and if so attempts to extract the β_r's from list names such as BETA0, BETA1, and so on. If the extraction is successful, then a list of L-moments similar to lmom.ub is returned. If the extraction was not successful, then an R list name betas is checked; if betas is found, then this vector of PWMs is used to compute the L-moments. If pwm is a list but can not be routed in the function, a warning is made and NULL is returned. If the pwm argument is a vector, then this vector of PWMs is used. to compute the L-moments are returned.

Value

One of two R lists are returned. Version I is

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.

Version II is

lambdas

The L-moments.

ratios

The L-moment ratios.

source

Source of the L-moments “pwm2lmom”.

Author(s)

W.H. Asquith

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, v. 15, pp. 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, v. 52, pp. 105–124.

See Also

lmom.ub, pwm.ub, pwm, lmom2pwm

Examples

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3
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D <- c(123,34,4,654,37,78)
pwm2lmom(pwm.ub(D))
pwm2lmom(pwm(D))
pwm2lmom(pwm(rnorm(100)))

lmomco documentation built on Nov. 17, 2017, 7:25 a.m.