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

Joe (2014, pp. 65–66) suggests two quantile-based measures of *bivariate skewness* defined for uniform random variables *U* and *V* combined as either *ψ_{u+v-1} = u + v - 1* or *ψ_{u-v} = u - v* for which the *\mathrm{E}[u] = \mathrm{E}[v] = 0*. The bivariate skewness is the quantity *η*:

*η(p; ψ) = \frac{x(1-p) - 2x(\frac{1}{2}) + x(p)}{x(1-p) - x(p)} \mbox{,}*

where *0 < p < \frac{1}{2}*, *x(F)* is the quantile function for nonexceedance probability *F* for either the quantities *X = ψ_{u+v-1}* or *X = ψ_{u-v}* using either the empirical quantile function or a fitted distribution. Joe (2014, p. 66) reports that *p = 0.05* to “achieve some sensitivity to the tails.” How these might be related (intuitively) to L-coskew (see function `lcomoms2()`

of the lmomco package) of the L-comoments or bivariate L-moments (`bilmoms`

) is unknown, but see the **Examples** section of `joeskewCOP`

.

Structurally the above definition for *η* based on quantiles is oft shown in comparative literature concerning L-moments. But why stop there? Why not compute the L-moments themselves to arbitrary order for *η* by either definition (the `uvlmoms`

variation)? Why not fit a distribution to the computed L-moments for estimation of *x(F)*? Or simply compute “skewness” according to the definition above (the `uvskew`

variation).

1 2 3 |

`u` |
Nonexceedance probability |

`v` |
Nonexceedance probability |

`umv` |
A logical controlling the computation of |

`p` |
A suggested |

`type` |
The |

`getlmoms` |
A logical triggering whether the L-moments of either |

`...` |
Additional arguments to pass to the lmomco function |

An **R** `list`

of the univariate L-moments of *η* is returned (see documentation for `lmoms`

in the lmomco package). Or the skewness of *η* can be either (1) based on the empirical distribution based on plotting positions by the `quantile`

function in **R** using the `type`

as described, or (2) based on the fitted quantile function for the parameters of a distribution for the lmomco package.

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.

Joe, H., 2014, Dependence modeling with copulas: Boca Raton, CRC Press, 462 p.

1 2 3 4 5 6 7 8 9 10 11 12 13 | ```
## Not run:
set.seed(234)
UV <- simCOP(n=100, cop=GHcop, para=1.5, graphics=FALSE)
lmr <- uvlmoms(UV); print(lmr) # L-kurtosis = 0.16568268
uvskew(UV, p=0.10) # -0.1271723
uvskew(UV, p=0.10, type="gno") # -0.1467011
## End(Not run)
## Not run:
pss <- seq(0.01,0.49, by=0.01)
ETA <- sapply(1:length(pss), function(i) uvskew(UV, p=pss[i], type=5, uvm1=FALSE) )
plot(pss, ETA, type="l", xlab="P FACTOR", ylab="BIVARIATE SKEWNESS") #
## End(Not run)
``` |

wasquith/copBasic documentation built on Nov. 20, 2019, 5:12 a.m.

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