w.hist: weighted histogram
In Weighted.Desc.Stat: Weighted Descriptive Statistics

Description Usage Arguments Details Warning Author(s) Examples

Assume that x=(x_1, x_2, \cdots , x_n) is the observed value of a random sample from a fuzzy population. In classical and usual random sample, the degree of belonging x_i into the random sample is equal to 1, for 1 ≤q i ≤q n. But considering fuzzy population, we denote the degree of belonging x_i into the fuzzy population (or into the observed value of random sample) by μ_i which is a real-valued number from [0,1]. Therefore in such situations, it is more appropriate that we show the observed value of the random sample by notation \{ (x_1, μ_1), (x_2, μ_2), \cdots , (x_n, μ_n) \} which we called it real-valued fuzzy data. This function drow the weighted histogram for a vector-valued data by considering a vector-valued weight. The weighted histogram containes several classical histograms which are depicted on one two-dimentional sorface. Each classical histogram drown only for the elements of real-value fuzzy data set which their weights are bigger than a cut point belongs to (0,1].

1	w.hist(x, mu, breaks, cuts, ylim = NULL, freq = NULL, lwd = NULL)

`x`	A vector-valued numeric data for which the weighted histogram is desired by considering their weights.
`mu`	A vector of weights of the real-value fuzzy data. The length of this vector must be equal to the length of x and each element of it is belongs to interval [0,1].
`breaks`	a vector giving the breakpoints between the weighted histogram cells.
`cuts`	a vector giving the cut-points between (to determine) the classical histograms in the desired weighted histogram.
`freq`	logical; if TRUE, the histogram graphic is a representation of frequencies, the counts component of the result; if FALSE, probability densities, component density, are plotted (so that the histogram has a total area of one). Defaults to TRUE if and only if breaks are equidistant (and probability is not specified).
`ylim`	numeric vector of length 2 giving the y limits for the plot. Unused if add = TRUE.
`lwd`	The line width, a positive number, defaulting to 1. The interpretation is device-specific, and some devices do not implement line widths less than one.

The arguments of the weighted histogram can be extended similar to the arguments of usual histogram which is detailed in function "hist" from "graphics" package.

The length of x and mu must be equal. Also, each element of mu must be in interval [0,1].

Abbas Parchami

Department of Statistics, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman, Kerman, Iran

n = 5000
x = rnorm(n,17,1)
x[x<14 | x>20] = NA
range(x)
mu = runif(n,0,1)
bre = seq(from=14,to=20,len=18)
cu = seq(from=0,to=1,len=10)
w.hist(x, mu, breaks=bre, cuts=cu, ylim=c(0,n/7), lwd = 2)

## The function is currently defined as
function(x, mu, breaks, cuts, ylim = NULL, freq = NULL, lwd = NULL) 
{
Gray = paste("gray", round(seq(from=10, to=100, len=length(cuts)-1)), sep="")
hist(x, col=Gray[1], xlim=range(breaks), ylim=ylim, breaks=breaks, freq=freq, lwd=lwd)
i=2
while(i<=length(cuts))
{
X=x
X[(X*(mu>=cuts[i]))==0]=NA
hist(X, col=Gray[i], xlim=range(breaks), ylim=ylim, breaks=breaks, freq=freq, lwd=lwd, add=TRUE)
i=i+1
}
}