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

Compute the L-comoment coefficients from an L-comoment matrix of order *k ≥ 2* and the *k = 2* (2nd order) L-comoment matrix. However, if the first argument is 1st-order then the coefficients of L-covariation are computed. The function requires that each matrix has already been computed by the function `Lcomoment.matrix`

.

1 | ```
Lcomoment.coefficients(Lk, L2)
``` |

`Lk` |
A |

`L2` |
A |

The coefficient of L-variation is computed by `Lcomoment.coefficients(L1,L2)`

where `L1`

is a 1st-order L-moment matrix and `L2`

is a *k = 2* L-comoment matrix. Symbolically, the coefficient of L-covariation is

* \hat{τ}_{[12]} = \frac{\hat{λ}_{2[12]}}
{\hat{λ}_{1[12]}} \mbox{.}*

The higher L-comoment coefficients (L-coskew, L-cokurtosis, ...) are computed by the function `Lcomoment.coefficients(L3,L2)`

(*k=3*), `Lcomoment.coefficients(L4,L2)`

(*k=4*), and so on. Symbolically, the higher L-comoment coefficients for *k ≥ 3* are

* \hat{τ}_{k[12]} = \frac{\hat{λ}_{k[12]}}
{\hat{λ}_{2[12]}}\mbox{.}*

Finally, the usual univariate L-moment ratios as seen from `lmom.ub`

or `lmoms`

are along the diagonal. The `Lcomoment.coefficients`

function does not make use of `lmom.ub`

or `lmoms`

.

An **R** `list`

is returned.

`type` |
The type of L-comoment representation in the matrix: “Lcomoment.coefficients”. |

`order` |
The order of the coefficients. |

`matrix` |
A |

The function begins with a capital letter. This is intentionally done so that lower case namespace is preserved. By using a capital letter now, then `lcomoment.coefficients`

remains an available name in future releases.

W.H. Asquith

Asquith, W.H., 2011, Distributional analysis with L-moment statistics using the R environment for statistical computing: Createspace Independent Publishing Platform, ISBN 978–146350841–8.

Serfling, R., and Xiao, P., 2007, A contribution to multivariate L-moments—L-comoment matrices: Journal of Multivariate Analysis, v. 98, pp. 1765–1781.

`Lcomoment.matrix`

, `Lcomoment.coefficients`

1 2 3 4 5 6 | ```
D <- data.frame(X1=rnorm(30), X2=rnorm(30), X3=rnorm(30))
L1 <- Lcomoment.matrix(D,k=1)
L2 <- Lcomoment.matrix(D,k=2)
L3 <- Lcomoment.matrix(D,k=3)
LkLCV <- Lcomoment.coefficients(L1,L2)
LkTAU3 <- Lcomoment.coefficients(L3,L2)
``` |

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