rden: Specific (contaminated) distributions

In DeconWK: Deconvolution by Weighted Kernels

Description

Density functions and random generation from the distributions considered in Hazelton and Turlach (2009); details of the distributions (all Gaussian mixtures) are given on pages 221–222.

Usage

dden(eval, DEN=1, sigma=0)
rden(N, DEN = 1, sigma=0)

Arguments

eval	vector of quantiles.
N	number of observations to be simulated; Should be a single number.
DEN	density to simulate from; possible values are 1, 2, 3 and 4 corresponding to the densities described in the paper.
sigma	the standardard deviation of the contaminating measurement error.

Details

The generated random variates are from X+Z where the distribution of X is determined by the argument DEN and Z has a normal distribution with mean zero and standard deviation sigma; X and Z are independent.

Value

A vector with the generated random variates.

Author(s)

Martin L Hazelton [e-mail]

References

Hazelton, M.L. and Turlach, B.A. (2009). Nonparametric density deconvolution by weighted kernel estimators, Statistics and Computing 19(3): 217–228. http://dx.doi.org/10.1007/s11222-008-9086-7.

Examples

  ##
  ## Figure 1 from paper
  ##
  opar <- par(mfrow=c(2,2))
  eval1 <- seq(-4,4,length=200)
  eval2 <- eval1
  eval3 <- seq(-8,7,length=300)
  eval4 <- seq(-2,30,length=320)

  plot(eval1,dden(eval1,DEN=1),type="l",xlab="",ylab="density")
  lines(eval1,dden(eval1,DEN=1,sigma=0.5),lty=3,lwd=1.25)
  lines(eval1,dden(eval1,DEN=1,sigma=0.5/sqrt(2.5)),lty=2,lwd=1.25)
  lines(eval1,dden(eval1,DEN=1,sigma=0.5*sqrt(2)),lty=4,lwd=1.25)
  title("Density 1")
  plot(eval2,dden(eval2,DEN=2),type="l",xlab="",ylab="density")
  lines(eval2,dden(eval2,DEN=2,sigma=sqrt(51/300)),lty=3,lwd=1.25)
  lines(eval2,dden(eval2,DEN=2,sigma=sqrt(51/300)/sqrt(2.5)),lty=2,lwd=1.25)
  lines(eval2,dden(eval2,DEN=2,sigma=sqrt(51/300)*sqrt(2)),lty=4,lwd=1.25)
  title("Density 2")
  plot(eval3,dden(eval3,DEN=3),type="l",xlab="",ylab="density")
  lines(eval3,dden(eval3,DEN=3,sigma=sqrt(1.8125)),lty=3,lwd=1.25)
  lines(eval3,dden(eval3,DEN=3,sigma=sqrt(1.8125)/sqrt(2.5)),lty=2,lwd=1.25)
  lines(eval3,dden(eval3,DEN=3,sigma=sqrt(1.8125)*sqrt(2)),lty=4,lwd=1.25)
  title("Density 3")
  plot(eval4,dden(eval4,DEN=4),type="l",xlab="",ylab="density")
  lines(eval4,dden(eval4,DEN=4,sigma=sqrt(2.516)),lty=3,lwd=1.25)
  lines(eval4,dden(eval4,DEN=4,sigma=sqrt(2.516)/sqrt(2.5)),lty=2,lwd=1.25)
  lines(eval4,dden(eval4,DEN=4,sigma=sqrt(2.516)*sqrt(2)),lty=4,lwd=1.25)
  title("Density 4")
  par(opar)

DeconWK documentation built on May 2, 2019, 6:08 p.m.