quacau

Nonexceedance probability ($0 \le F \le 1$).

The parameters from <code><a href="/link/parcau?package=lmomco&version=0.88" rd-options="" data-mini-rdoc="lmomco::parcau">parcau</a></code> or <code><a href="/link/vec2par?package=lmomco&version=0.88" rd-options="" data-mini-rdoc="lmomco::vec2par">vec2par</a></code>.

para

This function computes the quantiles of the Cauchy distribution given
parameters ($\xi$ and $\alpha$) of the distribution provided by
<code><a href="/link/vec2par?package=lmomco&version=0.88" rd-options="" data-mini-rdoc="lmomco::vec2par">vec2par</a></code>. The quantile function of the distribution is$$x(F) = \xi + \alpha \times \tan(\pi(F-0.5)) \mbox{,}$$where $x(F)$ is the quantile for nonexceedance probability $F$,
$\xi$ is a location parameter and $\alpha$ is a scale parameter.
R supports the quantile function of the Cauchy distribution through
<code>qcauchy</code>. This function does not use <code>qcauchy</code> because
<code>qcauchy</code> does not return <code>Inf</code> for $F = 1$ although it
returns <code>-Inf</code> for $F = 0$.

distribution

The package implements the statistical theory of L-moments including 
 L-moment estimation, probability-weighted moment estimation, parameter estimation 
 for numerous familiar and not-so-familiar distributions, and L-moment estimation 
 for the same distributions from the parameters. L-moments are derived from the 
 expectations of order statistics and are linear with respect to the probability- 
 weighted moments. L-moments are directly analogous to the well-known product 
 moments; however, L-moments have many advantages including unbiasedness, 
 robustness, and consistency with respect to the product moments. This package 
 is oriented around the FORTRAN algorithms of J.R.M. Hosking, and the 
 nomenclature for many of the functions parallels that of the Hosking library. 
 However, numerous extensions are made to aid in expand of the breadth and ease
 of L-moment application. Much theoretical extension of L-moment theory has 
 occurred in recent years. E.A.H. Elamir and A.H. Seheult have developed the 
 trimmed L-moments, which are implemented in this package. Further, recent 
 developments by Robert Serfling and Peng Xiao have extended L-moments into 
 multivariate space; the so-called sample L-comoments are implemented here. The 
 supported distributions with moment type shown as L (L-moments) or TL (trimmed 
 L-moments) and additional support for right-tail censoring ([RC]) include:
 Cauchy(TL), Exponential(L), Gamma(L), Generalized Extreme Value(L),
 Generalized Lambda(L & TL), Generalized Logistic (L), Generalized Normal(L),
 Generalized Pareto(L[RC] & TL), Gumbel(L), Normal(L), Kappa(L),
 Pearson Type III(L), Reverse Gumbel(L[RC]), Wakeby(L), and Weibull(L).

quacau: Quantile Function of the Cauchy Distribution

Description

Usage

Arguments

Value

References

See Also

Examples