fcenLR transformation (functional)
fcenLR[lambda] transformation: mapping from B^2(lambda) into L^2(lambda)
fcenLR(z, z_step, density)
z |
grid of points defining the abscissa |
z_step |
step of the grid of the abscissa |
density |
grid evaluation of the lambda-density |
|
grid evaluation of the lambda-density in L^2(lambda) |
R. Talskatalskarenata@seznam.cz, A. Menafoglio, K. Hronkarel.hron@upol.cz, J. J. Egozcue, J. Palarea-Albaladejo
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
# Example (normal density) t = seq(-4.7,4.7, length = 1000) t_step = diff(t[1:2]) mean = 0; sd = 1.5 f = dnorm(t, mean, sd) f1 = f/trapzc(t_step,f) f.fcenLR = fcenLR(t,t_step,f) f.fcenLRinv = fcenLRinv(t.fine,t_step,f.fcenLR) plot(t,f.fcenLR, type="l",las=1, ylab="fcenLR(density)", cex.lab=1.2,cex.axis=1.2, col="darkblue",lwd=2) abline(h=0, col="red") plot(t,f.fcenLRinv, type="l",las=1, ylab="density",cex.lab=1.2,cex.axis=1.2, col="darkblue",lwd=2,lty=1) lines(t,f1,lty=2,lwd=2,col="gold")
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