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 rd-options="" href="/link/pp?package=lmomco&version=2.2.5" 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 $pp'_r = r/(n+1)$ (Weibull plotting position) and the Beta quantile function is $pp_r(F) = IIB(F, r, n+1-r)$, where $F$ represents the nonexceedance probability of the plotting position.  $IIB$ is the &#147;inverse of the incomplete beta function&#148; or the quantile function of the Beta distribution as provided in <span style="R">R</span> by <code>qbeta(f, a, b)</code>.  If $F=0.5$, then the median is returned but that is conveniently implemented in <code><a rd-options="" href="/link/pp.median?package=lmomco&version=2.2.5" data-mini-rdoc="lmomco::pp.median">pp.median</a></code>.   Readers might consult Gilchrist (2011, chapter 12) and Karian and Dudewicz (2011, p. 510).


plotting position

rankit

Extensive functions for L-moments (LMs) and probability-weighted moments (PWMs), parameter estimation for distributions, LM computation for distributions, and L-moment ratio diagrams. Maximum likelihood and maximum product of spacings estimation are also available. LMs for right-tail and left-tail censoring by known or unknown threshold and by indicator variable are available. Asymmetric (asy.) trimmed LMs (TL-moments, TLMs) are supported. LMs of residual (resid.) and reversed (rev.) resid. life are implemented along with 13 quantile function operators for reliability and survival analyses.  Exact analytical bootstrap estimates of order statistics, LMs, and variances-covariances of LMs are provided. The Harri-Coble Tau34-squared Normality Test is available. Distribution support with "L" (LMs), "TL" (TLMs) and added (+) support for right-tail censoring (RC) encompasses: Asy. Exponential (Exp.) Power [L], Asy. Triangular [L], Cauchy [TL], Eta-Mu [L], Exp. [L], Gamma [L], Generalized (Gen.) Exp. Poisson [L], Gen. Extreme Value [L], Gen. Lambda [L,TL], Gen. Logistic [L), Gen. Normal [L], Gen. Pareto [L+RC, TL], Govindarajulu [L], Gumbel [L], Kappa [L], Kappa-Mu [L], Kumaraswamy [L], Laplace [L], Linear Mean Resid. Quantile Function [L], Normal [L], 3-p log-Normal [L], Pearson Type III [L], Rayleigh [L], Rev.-Gumbel [L+RC], Rice/Rician [L], Slash [TL], 3-p Student t [L], Truncated Exponential [L], Wakeby [L], and Weibull [L]. Multivariate sample L-comoments (LCMs) are implemented to measure asymmetric association.

William Asquith

lmomco

L-Moments, Censored L-Moments, Trimmed L-Moments, L-Comoments,
and Many Distributions

pp.f function


There are two major forms (outside of the general plotting-position formula <code><a rd-options='' href='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 $pp'_r = r/(n+1)$ (Weibull plotting position) and the Beta quantile function is $pp_r(F) = IIB(F, r, n+1-r)$, where $F$ represents the nonexceedance probability of the plotting position.  $IIB$ is the &#147;inverse of the incomplete beta function&#148; or the quantile function of the Beta distribution as provided in <span style="R">R</span> by <code>qbeta(f, a, b)</code>.  If $F=0.5$, then the median is returned but that is conveniently implemented in <code><a rd-options='' href='pp.median'>pp.median</a></code>.   Readers might consult Gilchrist (2011, chapter 12) and Karian and Dudewicz (2011, p. 510).


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

Description

Usage

Arguments

Value

References

See Also

Examples