Histogram

Creating Histogram function using Min-max transformation.

The histogram plot of a vector or a data feature is to create bins, which is to create a series of interval, for the range of data values, and to count how many data values fall into each bins.

I create bins as the following;

Suppose we have $M$ bins, then

$$B_1 = [0,\frac{1}{M}), B_2 = [\frac{1}{M}, \frac{2}{M}), …, B_{M-1} = [\frac{M-2}{M}, \frac{M-1}{M}), B_{M} = [\frac{M-1}{M}, 1)$$

To create histogram function with the bins, I wanted to transform the data elements in interval $(0,1)$, so I can put them into each bins.

That’s why I used Min-max transformation, which makes the data reducing to a scale between 0 and 1.

Min-max transformation is the following formula;

$$z = \frac{x-min(x)}{max(x)-min(x)}$$

The below codes are the implementation of creating histogram plot in R. I used the values from CLT posts.

CLT link


Hist <- function(vec,bin){
  vec.minmax <- (vec - min(vec))/(max(vec)-min(vec)) #min-max transformation of the vector or the values
  
  vec.bins <- rep(0,bin)
  for(i in 1:bin){
  	#find the values that is the closest to the value of each boundary of the bins
    vec.bins[i] <- vec[which(abs(vec.minmax - i/bin) == min(abs(vec.minmax - i/bin)))]
  }
  
  dat <- data.frame(x=vec.bins, freq=0)
  for(i in 1:bin){
  	#put the values into each bins associateed
    dat[i,2] <- length(which(vec.minmax > (i-1)/bin & vec.minmax <= i/bin))
  }
  
  #plotting
  p <- dat %>% ggplot(aes(x=x, y=freq)) + geom_bar(stat="identity", position=position_dodge(width=0.5)) + theme_bw()

  return(p)
}