quaray

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

The parameters from <code><a href="/link/parray?package=lmomco&version=1.3.3" rd-options="" data-mini-rdoc="lmomco::parray">parray</a></code> or similar.

para

This function computes the quantiles of the Rayleigh distribution given
parameters ($\xi$ and $\alpha$) of the distribution computed by
<code><a href="/link/parray?package=lmomco&version=1.3.3" rd-options="" data-mini-rdoc="lmomco::parray">parray</a></code>.
The quantile function of the distribution is$$x(F) = \xi + \sqrt{-2\alpha^2\log(1-F)} \mbox{,}$$where $x(F)$ is the quantile for nonexceedance probability $F$,
$\xi$ is a location parameter, and $\alpha$ is a scale parameter.

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; 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. The method of
        L-moments can out perform the method of maximum likelihood. The
        lmomco package historically is oriented around canonical
        FORTRAN algorithms of J.R.M. Hosking, and the nomenclature for
        many of the functions parallels that of the Hosking library,
        which later became available in the lmom package. However, vast
        arrays of various extensions and curiosities are added by the
        author to aid and expand of the breadth of L-moment
        application. Such extensions include venerable statistics as
        Sen weighted mean, Gini mean difference, plotting positions,
        and conditional probability adjustment. Much extension of
        L-moment theory has occurred in recent years, including
        extension of L-moments into right-tail and left-tail censoring
        by known or unknown censoring threshold and also by indicator
        variable. E.A.H. Elamir and A.H. Seheult have developed the
        trimmed L-moments, which are implemented in this package.
        Further, Robert Serfling and Peng Xiao have extended L-moments
        into multivariate space; the so-called sample L-comoments are
        implemented here and might have considerable application in
        copula theory because they measure asymmetric correlation and
        higher co-moments. 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), Kappa (L), Kumaraswamy (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).

quaray: Quantile Function of the Rayleigh Distribution

Description

Usage

Arguments

Value

References

See Also

Examples