quacau

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

The parameters from <code><a href="/link/parcau?package=lmomco&version=1.7.3" rd-options="" data-mini-rdoc="lmomco::parcau">parcau</a></code> or <code><a href="/link/vec2par?package=lmomco&version=1.7.3" rd-options="" data-mini-rdoc="lmomco::vec2par">vec2par</a></code>.

para

A logical controlling whether the parameters and checked for validity. Overriding of this check might be extremely important and needed for use of the distribution quantile function in the context of TL-moments with nonzero trimming.

paracheck

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=1.7.3" 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
        in R 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; choice of either
        can be made by mathematical convenience. 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, and the method
        of L-moments can out perform the method of maximum likelihood.
        The lmomco package historically was originally oriented around
        canonical FORTRAN algorithms of Hosking's library, and the
        nomenclature for many of the functions parallels those of the
        Hosking library. Hosking's algorithms later became available in
        the lmom package. However, vast extensions, components,
        concepts, and other L-moment curiosities are added to lmomco to
        aid and expand the breadth of L-moment applications. Such
        extensions include venerable statistics as Sen weighted mean,
        Gini mean difference, plotting positions, and conditional
        probability adjustment. The plotting of L-moment ratio diagrams
        is directly supported in this package. Computations of
        L-moments for right-tail and left-tail censoring by known or
        unknown censoring threshold (Hosking) and also by indicator
        variable also are available. Trimmed L-moments are supported as
        is numerical integration of quantile functions to dynamically
        compute trajectories of select TL-moment ratios for the
        construction of TL-moment ratio diagrams. L-moments have been
        extended into multivariate space; the so-called sample
        L-comoments are implemented and might have considerable
        application in copula theory because they measure asymmetric
        correlation and higher comoments or comovements of variables.
        The package supports exact analytical boot strap estimates of
        order statistics, L-moments, and variances-covariances of
        L-moments. The package provides the Harri-Coble Tau34-squared
        Test for Normality that uses only the sample L-skew and
        L-kurtosis. The package supports the following distributions
        with moment type shown as "L" (L-moments) or "TL" (trimmed
        L-moments) and additional support for right-tail censoring
        ([RC]) include: Asymmetric Exponential Power (L), Cauchy (TL),
        Eta-Mu (L), 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), Kappa (L), Kappa-Mu (L), Kumaraswamy (L), Laplace
        (L), Normal (L), 3-parameter log-Normal (L), Pearson Type III
        (L), Rayleigh (L), Reverse Gumbel (L[RC]), Rice/Rician (L),
        Truncated Exponential (L), Wakeby (L), and Weibull (L).

quacau: Quantile Function of the Cauchy Distribution

Description

Usage

Arguments

Value

References

See Also

Examples