Description Usage Arguments Value Author(s) See Also Examples

This function computes the nonexceedance probability of a given quantile from a linear weighted combination of two quantile functions but accomplishes this from the perspective of cumulative distribitution functions (see `par2qua2`

). However, for the current implementation simply `uniroot`

'ing of a internally declared function and `par2qua2`

is made.

The distributions are specified by the two parameter object arguments in usual lmomco style. The left-tail parameter object is the distribution obviously governing the left tail; the right-tail parameter object is of course governs the right tail. The quantile function algebra is

* Q(F) = (1-F) \times Q_{\triangleleft}(F) + F \times Q_{\triangleright}(F)\mbox{,}*

where *Q(F)* is the equivalent quantile for nonexceedance probability *F* computed by the tail weigthing. *Q_{\triangleleft}(F)* is the left-tail quantile function; *Q_{\triangleright}(F)* is the right-tail quantile function. The `par2cdf2`

function inverses the above equation for *F*. Parameter objects are discussed in `lmom2par`

and `vec2par`

. If the optional `weight`

argument is provided, then the multiplication of `1-F`

or `F`

is replaced by `1-weight`

or `weight`

, respectively. If `weight=0`

, then the quantiles for the right tail are returned, and if `weight=1`

, then the quantiles for the left tail are returned. The biggest feature on this function is that a vector of real values is used as the primary argument and not a vector of *F*.

A word of caution. The resulting weighted quantile function is not checked for monotonic increase with *F*. This is a required property of quantile functions.

1 |

`x` |
A real value vector. |

`leftpara` |
The left-tail parameters from |

`rightpara` |
The right-tail parameters from |

`weight` |
An optional weighting argument to use in lieu of the |

`...` |
The additional arguments are passed to the cumulative distribution function such as |

Nonexceedance probabilities (*0 ≤ F ≤ 1*) for `x`

from the two distributions.

W.H. Asquith

1 2 3 4 5 |

lmomco documentation built on May 19, 2017, 4:27 p.m.

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