pp.f

There are two major forms (outside of the general plotting-position formula <code>pp</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 &#8220;inverse of the incomplete beta function&#8221; or the quantile function of the Beta distribution as provided in R by <code>qbeta(f, a, b)</code>. If \(F=0.5\), then the median is returned but that is conveniently implemented in <code>pp.median</code>. Readers might consult Gilchrist (2011, chapter 12) and Karian and Dudewicz (2011, p. 510).

plotting position

rankit

Extensive functions for Lmoments (LMs) and probability-weighted moments (PWMs),
distribution parameter estimation, LMs for distributions, LM ratio diagrams, multivariate
Lcomoments, and asymmetric (asy) trimmed LMs (TLMs). Maximum likelihood and
maximum product spacings estimation are available. Right-tail and left-tail LM censoring
by threshold or indicator variable are available. LMs of residual (resid) and reversed
(rev) residual life are implemented along with 13 quantile operators for reliability analyses.
Exact analytical bootstrap estimates of order statistics, LMs, and LM var-covars are available.
Harri-Coble Tau34-squared Normality Test is available. Distributions with L, TL, and added
(+) support for right-tail censoring (RC) encompass: 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 Residual Quantile Function [L], Normal [L],
3p log-Normal [L], Pearson Type III [L], Polynomial Density-Quantile 3 and 4 [L],
Rayleigh [L], Rev-Gumbel [L+RC], Rice [L], Singh Maddala [L], Slash [TL], 3p Student t [L],
Truncated Exponential [L], Wakeby [L], and Weibull [L].

William Asquith

lmomco

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

pp.f function

<dl> <dt>f</dt>
<dd>A nonexceedance probability.</dd> <dt>x</dt>
<dd>A vector of data. The ranks and the length of the vector are computed within the function.</dd></dl>

Arguments

Author

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

<dl>

 <dt>f</dt>
<dd>A nonexceedance probability.</dd>

 <dt>x</dt>
<dd>A vector of data. The ranks and the length of the vector are computed within the function.</dd>

</dl>

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

Description

Usage

Value

Arguments

Author

References

See Also

Examples