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)

Arguments

A real value vector. 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 <- 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)
# F <- nonexceeds()
# plot(F, qlmomco(F,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.
# ## End(Not run)