percentile-based function

The Percentile-based Distribution

Density, distribution function, quantile function and random generation for the percentile-based distribution.

dPercbas(x, xi, F)
pPercbas(q, xi, F)
qPercbas(p, xi, F)
rPercbas(n, xi, F)

Arguments

• x, q: vector of quantiles
• p: vector of probabilitiies
• n: number of observations. If length(n) > 1, the length is taken to be the number required.
• xi: Strictly increasing vector of percentiles corresponding to the cumulative probabilities given in F. Of same length as F.
• F: a k-length strictly increasing vector of cumulative probabilities, with xi[1]=0 and xi[k]=1.

Details

The percentile-based distribution is defined by the quantiles xi that correspond to the cumulative probabilities given in F. The continuous distribution is obtained by linear interpolation of the cdf.

Returns

dll gives the density, pll gives the distribution function, qll gives the quantile function, and rll generates random deviates.

The length of the result is determined by n for rPercbas, and by the length of x, q and p for the other functions.

Author(s)

Lauri Mehtatalo <lauri.mehtatalo@uef.fi >

Examples

d0<-seq(0,30,0.01)
d<-c(5,7,10,11,11.7,13,15,19,22,24,25,28.5)
plot(d0,pPercbas(d0,d),type="l")
hist(rPercbas(1000,d),breaks=seq(0,30,1),freq=FALSE,ylim=c(0,0.15))
lines(d0,dPercbas(d0,d),col="red")

References

Borders B. E., Souter R. A., Bailey. R. L., and Ware, K. D. 1987. Percentile-based distributions characterize forest stand tables. Forest Science 33(2): 570-576.

Mehtatalo, L. 2005. Localizing a predicted diameter distribution using sample information. Forest Science 51(4): 292--302.

Mehtatalo, Lauri and Lappi, Juha 2020a. Biometry for Forestry and Environmental Data: with examples in R. New York: Chapman and Hall/CRC. 426 p. tools:::Rd_expr_doi("10.1201/9780429173462")

Mehtatalo, Lauri and Lappi, Juha 2020b. Biometry for Forestry and Environmental Data: with examples in R. Full Versions of The Web Examples. Available at http://www.biombook.org.