pp.f

A vector of data. The ranks and the length of the vector are computed within the function.

There are two major forms (outside of the general plotting-position formula <code><a href="/link/pp?package=lmomco&version=2.0.1" rd-options="" data-mini-rdoc="lmomco::pp">pp</a></code>) for estimation of the $p_r$th probability of the $r$th order statistic for a sample of size $n$: the mean is $p'_r = r/(n+1)$ (Weibull plotting position) and the median is $p^\star_r = IIB(0.5, r, n+1-r)$, where $f$ represents the nonexceedance probability of the plotting position.  $IIB$ is the <dquote>inverse of the incomplete beta function</dquote> or the quantile function of the beta distribution as provided by <code>qbeta(f, a, b)</code>.  If $f=0.5$, then the median is returned but conveniently implemented in <code><a href="/link/pp.median?package=lmomco&version=2.0.1" rd-options="" data-mini-rdoc="lmomco::pp.median">pp.median</a></code>.   See Gilchrist (2011, chapter 12, p. 510 in Karian and Dudewicz, 2011).

plotting position

rankit

The package is a comparatively comprehensive implementation of the theory of L-moments. L-moment, probability-weighted moment (PWM), and parameter estimation for numerous familiar and not-so-familiar distributions are provided. L-moment estimate for the same distributions are provided. L-moments are analogous to product moments; however, L-moments have many advantages including unbiasedness, robustness, and consistency. L-moments can outperform maximum likelihood for small to moderate samples. The package originally was originally oriented around circa 1996-FORTRAN algorithms by Hosking, and the nomenclature parallels that of Hosking. The Hosking algorithms later became available in the lmom package. However, vast extensions, components, concepts, more distributions, L-moment curiosities, and research topics are added. Such extensions the Sen weighted mean, Gini mean difference, plotting positions, and conditional probability adjustments. L-moment ratio diagrams are supported. L-moment support for right-tail and left-tail censoring by known or unknown censoring threshold and also by indicator variable. Asymmetric trimmed L-moments are supported as are numerical integration to dynamically compute trajectories of select TL-moment ratios for the construction of TL-moment ratio diagrams. L-moments have multi-variate analogs; the sample L-comoments are implemented and might have considerable application with copulas because L-comoments measure asymmetric association and higher comoments or comovements of variables. Support exists for exact analytical boot-strap estimates of order statistics, L-moments, and variances-covariances of L-moments. The Harri-Coble Tau34-squared Test for Normality using sample L-skew and L-kurtosis is available. Support for 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, is available: 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), Govindarajulu (L), 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), Slash (TL), 3-parameter Student T (L), Truncated Exponential (L), Wakeby (L), and Weibull (L).

pp.f: Quantile Function of the Ranks of Plotting Positions

Description

Usage

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References

See Also

Examples