frechet (version 0.3.0)

CreateDensity: Create density functions from raw data, histogram objects or frequency tables with bins

Description

Create kernel density estimate along the support of the raw data using the HADES method.

Usage

CreateDensity(
  y = NULL,
  histogram = NULL,
  freq = NULL,
  bin = NULL,
  optns = list()
)

Value

A list containing the following fields:

bw

The bandwidth used for smoothing.

x

A vector of length nRegGrid with the values of the KDE's support points.

y

A vector of length nRegGrid with the values of the KDE at the support points.

Arguments

y

A vector of raw readings.

histogram

A histogram object in R. Use this option when histogram object is only available, but not the raw data y. The default is NULL.

freq

A frequency vector. Use this option when frequency table is only available, but not the raw sample or the histogram object. The corresponding bin should be provided together. The default is NULL.

bin

A bin vector having its length with length(freq)+1. Use this option when frequency table is only available, but not the raw sample or the histogram object. The corresponding freq should be provided together.The default is NULL.

optns

A list of options control parameters specified by list(name=value). See `Details'.

Details

Available control options are

userBwMu

The bandwidth value for the smoothed mean function; positive numeric - default: determine automatically based on the data-driven bandwidth selector proposed by Sheather and Jones (1991)

nRegGrid

The number of support points the KDE; numeric - default: 101.

delta

The size of the bin to be used; numeric - default: diff(range(y))/1000. It only works when the raw sample is available.

kernel

smoothing kernel choice, "rect", "gauss", "epan", "gausvar", "quar" - default: "gauss".

infSupport

logical if we expect the distribution to have infinite support or not; logical - default: FALSE.

outputGrid

User defined output grid for the support of the KDE, it overrides nRegGrid; numeric - default: NULL.

References

• H.-G. Müller, J.L. Wang and W.B. Capra (1997). "From lifetables to hazard rates: The transformation approach." Biometrika 84, 881--892.

• S.J. Sheather and M.C. Jones (1991). "A reliable data-based bandwidth selection method for kernel density estimation." JRSS-B 53, 683--690.

• H.-G. Müller, U. Stadtmüller, and T. Schmitt. (1987) "Bandwidth choice and confidence intervals for derivatives of noisy data." Biometrika 74, 743--749.

Examples

### compact support case

# input: raw sample
set.seed(100)
n <- 100
x0 <-seq(0,1,length.out=51)
Y <- rbeta(n,3,2)
f1 <- CreateDensity(y=Y,optns = list(outputGrid=x0))

# input: histogram
histY <- hist(Y)
f2 <- CreateDensity(histogram=histY,optns = list(outputGrid=x0))

# input: frequency table with unequally spaced (random) bins
binY <- c(0,sort(runif(9)),1)
freqY <- c()
for (i in 1:(length(binY)-1)) {
  freqY[i] <- length(which(Y>binY[i] & Y<=binY[i+1]))
}
f3 <- CreateDensity(freq=freqY, bin=binY,optns = list(outputGrid=x0))

# plot
plot(f1$x,f1$y,type='l',col=2,lty=2,lwd=2,
     xlim=c(0,1),ylim=c(0,2),xlab='domain',ylab='density')
points(f2$x,f2$y,type='l',col=3,lty=3,lwd=2)
points(f3$x,f3$y,type='l',col=4,lty=4,lwd=2)
points(x0,dbeta(x0,3,2),type='l',lwd=2)
legend('topleft',
       c('true','raw sample','histogram','frequency table (unequal bin)'),
       col=1:4,lty=1:4,lwd=3,bty='n')

### infinite support case

# input: raw sample
set.seed(100)
n <- 200
x0 <-seq(-3,3,length.out=101)
Y <- rnorm(n)
f1 <- CreateDensity(y=Y,optns = list(outputGrid=x0))

# input: histogram
histY <- hist(Y)
f2 <- CreateDensity(histogram=histY,optns = list(outputGrid=x0))

# input: frequency table with unequally spaced (random) bins
binY <- c(-3,sort(runif(9,-3,3)),3)
freqY <- c()
for (i in 1:(length(binY)-1)) {
  freqY[i] <- length(which(Y>binY[i] & Y<=binY[i+1]))
}
f3 <- CreateDensity(freq=freqY, bin=binY,optns = list(outputGrid=x0))

# plot
plot(f1$x,f1$y,type='l',col=2,lty=2,lwd=2,
     xlim=c(-3,3),ylim=c(0,0.5),xlab='domain',ylab='density')
points(f2$x,f2$y,type='l',col=3,lty=3,lwd=2)
points(f3$x,f3$y,type='l',col=4,lty=4,lwd=2)
points(x0,dnorm(x0),type='l',lwd=2)
legend('topright',
       c('true','raw sample','histogram','frequency table (unequal bin)'),
       col=1:4,lty=1:4,lwd=3,bty='n')