# Create density functions from raw data, histogram objects or frequency tables with bins Create kernel density estimate along the support of the raw data using the HADES method. ```r CreateDensity( y = NULL, histogram = NULL, freq = NULL, bin = NULL, optns = list() ) ``` ## 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'. ## Returns 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. ## 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`. ## Examples ```r ### 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') ``` ## References * H.-G. Müller, J.L. Wang and W.B. Capra (1997). "From lifetables tohazard rates: The transformation approach." Biometrika 84, 881-892. * S.J. Sheather and M.C. Jones (1991). "A reliable data-based bandwidthselection method for kernel density estimation." JRSS-B 53, 683-690. * H.-G. Müller, U. Stadtmüller, and T. Schmitt. (1987) "Bandwidth choiceand confidence intervals for derivatives of noisy data." Biometrika 74,743-749.

CreateDensity function