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

Description

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

Usage

pp.f(f, x)

Arguments

A nonexceedance probability.

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

Value

An R vector is returned.

References

Gilchrist, W.G., 2000, Statistical modelling with quantile functions: Chapman and Hall/CRC, Boca Raton.

Karian, Z.A., and Dudewicz, E.J., 2011, Handbook of fitting statistical distributions with R: Boca Raton, FL, CRC Press.

Examples

Run this code

# NOT RUN {
X <- sort(rexp(10))
PPlo <- pp.f(0.25, X)
PPhi <- pp.f(0.75, X)
plot(c(PPlo,NA,PPhi), c(X,NA,X))
points(pp(X), X) # Weibull i/(n+1)
# }