lmomco (version 2.4.14)

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

Description

The median of a plotting position. The median is \(pp^\star_r = IIB(0.5, r, n+1-r)\). \(IIB\) 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). Readers might consult Gilchrist (2011, chapter 12) and Karian and Dudewicz (2011, p. 510). The \(pp'_r\) are known in some fields as “mean rankit” and \(pp^\star_r\) as “median rankit.”

Usage

pp.median(x)

Value

An R

vector is returned.

Arguments

x

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

Author

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.f

Examples

if (FALSE) {
X <- rexp(10)*rexp(10)
means  <- pp(X, sort=FALSE)
median <- pp.median(X)
supposed.median <- pp(X, a=0.3175, sort=FALSE)
lmr <- lmoms(X)
par <- parwak(lmr)
FF  <- nonexceeds()
plot(FF, qlmomco(FF, par), type="l", log="y")
points(means,  X)
points(median, X, col=2)
points(supposed.median, X, pch=16, col=2, cex=0.5)
# The plot shows that the median and supposed.median by the plotting-position
# formula are effectively equivalent. Thus, the partial application it seems
# that a=0.3175 would be good enough in lieu of the complexity of the
# quantile function of the Beta distribution.
}