eff.dens {Benchmarking}  R Documentation 
A method to estimate and plot kernel estimate of (Farrell) efficiencies taken into consideration that efficiencies are bounded either above (input direction) or below (output direction).
eff.dens(eff, bw = "nrd0") eff.dens.plot(obj, bw = "nrd0", ..., xlim, ylim, xlab, ylab)
eff 
Either a list of (Farrell) efficiencies or a Farrell
object returned from the method 
bw 
Bandwith, look at the documentation of 
obj 
Either an array of efficiencies or a list returned from

... 
Further arguments to the 
xlim 
Range on the xaxis; usualy not needed, just use the defaults. 
ylim 
Range on the xaxis; usualy not needed, just use the defaults. 
xlab 
Label for the xaxis. 
ylab 
Label for the yaxis. 
The calculation is based on a reflection method (Silverman
1986, 30) using the default window kernel and defult bandwidth (window
width) in the method density
.
The method eff.dens.plot
plot the density directly, and
eff.dens
just estimate the numerical density, and the result
can then either be plotted by plot
, corresponds to
eff.dens.plot
, or by lines as an overlay on an existing plot.
The return from eff.dens
is a list list(x,y)
with efficiencies and the corresponding density values.
The input efficiency is also bounded below by 0, but for normal firms an efficiency at 0 will not happen, i.e. the boundary is not effective, and therefore this boundary is not taken into consideration.
Peter Bogetoft and Lars Otto larsot23@gmail.com
B.W. Silverman (1986), Density Estimation for Statistics and Data Analysis, Chapman and Hall, London.
e < 1  rnorm(100) e[e>1] < 1 e < e[e>0] eff.dens.plot(e) hist(e, breaks=15, freq=FALSE, xlab="Efficiency", main="") den < eff.dens(e) lines(den,lw=2)