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Kernel Density Estimates of strictly positive distributions using FFT.

logdensity_fft.Rd

The function logdensity_fft computes kernel density estimates (KDE) of strictly positive distributions by performing the KDE via fast fourier transform utilizing the fft function. The syntax and function structure is largely borrowed from the function density in package stats.

Usage

logdensity_fft(
  x,
  bw = "nrd0",
  adjust = 1,
  kernel = "gaussian",
  weights = NULL,
  n = 512,
  from,
  to,
  cut = log(3),
  na.rm = FALSE
)

Arguments

x

the data from which the estimate is to be computed.

bw

the smoothing bandwidth to be used. Can also be can also be a character string giving a rule to choose the bandwidth. Like density defaults to "nrd0". All options in help(bw.nrd) are available as well as "bw.logCV" and "bw.logG".

adjust

the bandwidth used is actually adjust*bw.

kernel

a character string giving the smoothing kernel to be used. Choose from "gaussian", "epanechnikov", "triangular", "uniform", "laplace" and "logistic". Default value is "gaussian".

weights

numeric vector of non-negative observation weights of the same length as x.

n

the number of equally spaced points at which the density is to be estimated. Note that these are equally spaced in the log domain for logdensity_fft, and thus on a log scale when transformed back to the original domain.

from, to

the left and right-most points of the grid at which the density is to be estimated; the defaults are cut * bw outside of range(x).

cut

by default, the values of from and to are cut bandwidths beyond the extremes of the data

na.rm

logical; if TRUE, missing values are removed from x. If FALSE any missing values cause an error.

Value

An object with class "density". See help(density) for details.

References

Charpentier, A., & Flachaire, E. (2015). Log-transform kernel density estimation of income distribution. L'Actualite economique, 91(1-2), 141-159.

Cooley, J. W., & Tukey, J. W. (1965). An algorithm for the machine calculation of complex Fourier series. Mathematics of computation, 19(90), 297-301.

Wand, M. P., Marron, J. S., & Ruppert, D. (1991). Transformations in density estimation. Journal of the American Statistical Association, 86(414), 343-353.

See also

density, plot.density, logdensity, bw.nrd, bw.logCV, bw.logG.

Examples

logdensity_fft(abs(rnorm(100)), from =0.01, to= 2.5, kernel = 'logistic')
#> 
#> Call:
#> 	logdensity_fft(x = abs(rnorm(100)), kernel = "logistic", from = 0.01,     to = 2.5)
#> 
#> Data: abs(rnorm(100)) (100 obs.);	Bandwidth 'bw' = 0.3077
#> 
#>        x                 y          
#>  Min.   :0.01000   Min.   :0.04666  
#>  1st Qu.:0.03976   1st Qu.:0.45039  
#>  Median :0.15812   Median :0.61538  
#>  Mean   :0.45254   Mean   :0.67347  
#>  3rd Qu.:0.62872   3rd Qu.:0.74895  
#>  Max.   :2.50000   Max.   :3.53755