pp.f {lmomco}

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_rth probability of the rth 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

f

A nonexceedance probability.

x

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

Value

An R vector is returned.

Note

The function uses the R function rank, which has specific settings to handle tied data. For implementation here, the ties.method="first" method to rank is used.

Author(s)

W.H. Asquith

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.

See Also

pp, pp.median

Examples

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)