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

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{.}*

1 |

`pwm` |
A PWM object created by |

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.

One of two **R** `list`

s 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”. |

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, 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.

`lmom.ub`

, `pwm.ub`

, `pwm`

, `lmom2pwm`

1 2 3 4 |

lmomco documentation built on March 18, 2018, 1:45 p.m.

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