fcenLRu: fcenLRu transformation (functional) In robCompositions: Compositional Data Analysis

Description

fcenLR[u] transformation: mapping from B2(P) into unweigted L2(lambda)

Usage

 `1` ```fcenLRu(z, z_step, density, p) ```

Arguments

 `z` grid of points defining the abscissa `z_step` step of the grid of the abscissa `density` grid evaluation of the P-density `p` density of the reference measure P

Value

 `out` grid evaluation of the P-density in unweighted L2(lambda)

Author(s)

R. Talskatalskarenata@seznam.cz, A. Menafoglio, K. Hronkarel.hron@upol.cz, J. J. Egozcue, J. Palarea-Albaladejo

References

Talska, R., Menafoglio, A., Hron, K., Egozcue, J. J., Palarea-Albaladejo, J. (2020). Weighting the domain of probability densities in functional data analysis.Stat(2020). https://doi.org/10.1002/sta4.283

Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65``` ```# Common example for all transformations - fcenLR, fcenLRp, fcenLRu # Example (log normal distribution under the reference P) t = seq(1,10, length = 1000) t_step = diff(t[1:2]) # Log normal density w.r.t. Lebesgue reference measure in B2(lambda) f = dlnorm(t, meanlog = 1.5, sdlog = 0.5) # Log normal density w.r.t. Lebesgue reference measure in L2(lambda) f.fcenLR = fcenLR(t,t_step,f) # New reference given by exponential density p = dexp(t,0.25)/trapzc(t_step,dexp(t,0.25)) # Plot of log normal density w.r.t. Lebesgue reference measure # in B2(lambda) together with the new reference density p matplot(t,f,type="l",las=1, ylab="density",cex.lab=1.2,cex.axis=1.2, col="black",lwd=2,ylim=c(0,0.3),xlab="t") matlines(t,p,col="blue") text(2,0.25,"p",col="blue") text(4,0.22,"f",col="black") # Log-normal density w.r.t. exponential distribution in B2(P) # (unit-integral representation) fp = (f/p)/trapzc(t_step,f/p) # Log-normal density w.r.t. exponential distribution in L2(P) fp.fcenLRp = fcenLRp(t,t_step,fp,p) # Log-normal density w.r.t. exponential distribution in L2(lambda) fp.fcenLRu = fcenLRu(t,t_step,fp,p) # Log-normal density w.r.t. exponential distribution in B2(lambda) fp.u = fcenLRinv(t,t_step,fp.fcenLRu) # Plot layout(rbind(c(1,2,3,4),c(7,8,5,6))) par(cex=1.1) plot(t, f.fcenLR, type='l', ylab=expression(fcenLR[lambda](f)), xlab='t',las=1,ylim=c(-3,3), main=expression(bold(atop(paste('(a) Representation of f in ', L^2, (lambda)),'[not weighted]')))) abline(h=0,col="red") plot(t, f, type='l', ylab=expression(f[lambda]), xlab='t',las=1,ylim=c(0,0.4), main=expression(bold(atop(paste('(b) Density f in ', B^2, (lambda)),'[not weighted]')))) plot(t, fp, type='l', ylab=expression(f[P]), xlab='t', las=1,ylim=c(0,0.4), main=expression(bold(atop(paste('(c) Density f in ', B^2, (P)),'[weighted with P]')))) plot(t, fp.fcenLRp, type='l', ylab=expression(fcenLR[P](f[P])), xlab='t',las=1,ylim=c(-3,3), main=expression(bold(atop(paste('(d) Representation of f in ', L^2, (P)),'[weighted with P]')))) abline(h=0,col="red") plot(t, fp.u, type='l', ylab=expression(paste(omega^(-1),(f[P]))), xlab='t',las=1,ylim=c(0,0.4), main=expression(bold(atop(paste('(e) Representation of f in ', B^2, (lambda)),'[unweighted]')))) plot(t, fp.fcenLRu, type='l', ylab=expression(paste(fcenLR[u](f[P]))), xlab='t',las=1,ylim=c(-3,3), main=expression(bold(atop(paste('(f) Representation of f in ', L^2, (lambda)),'[unweighted]')))) abline(h=0,col="red") ```

robCompositions documentation built on Jan. 13, 2021, 10:07 p.m.