Discretize Continuous Random Variables
discretize puts observations from a continuous random variable
into bins and returns the corresponding vector of counts.
discretize2d puts observations from a pair of continuous random variables
into bins and returns the corresponding table of counts.
discretize( x, numBins, r=range(x) ) discretize2d( x1, x2, numBins1, numBins2, r1=range(x1), r2=range(x2) )
x |
vector of observations. |
x1 |
vector of observations for the first random variable. |
x2 |
vector of observations for the second random variable. |
numBins |
number of bins. |
numBins1 |
number of bins for the first random variable. |
numBins2 |
number of bins for the second random variable. |
r |
range of the random variable (default: observed range). |
r1 |
range of the first random variable (default: observed range). |
r2 |
range of the second random variable (default: observed range). |
The bins for a random variable all have the same width. It is determined by the length of the range divided by the number of bins.
discretize returns a vector containing the counts for each bin.
discretize2d returns a matrix containing the counts for each bin.
Korbinian Strimmer (http://www.strimmerlab.org).
# load entropy library
library("entropy")
### 1D example ####
# sample from continuous uniform distribution
x1 = runif(10000)
hist(x1, xlim=c(0,1), freq=FALSE)
# discretize into 10 categories
y1 = discretize(x1, numBins=10, r=c(0,1))
y1
# compute entropy from counts
entropy(y1) # empirical estimate near theoretical maximum
log(10) # theoretical value for discrete uniform distribution with 10 bins
# sample from a non-uniform distribution
x2 = rbeta(10000, 750, 250)
hist(x2, xlim=c(0,1), freq=FALSE)
# discretize into 10 categories and estimate entropy
y2 = discretize(x2, numBins=10, r=c(0,1))
y2
entropy(y2) # almost zero
### 2D example ####
# two independent random variables
x1 = runif(10000)
x2 = runif(10000)
y2d = discretize2d(x1, x2, numBins1=10, numBins2=10)
sum(y2d)
# joint entropy
H12 = entropy(y2d )
H12
log(100) # theoretical maximum for 10x10 table
# mutual information
mi.empirical(y2d) # approximately zero
# another way to compute mutual information
# compute marginal entropies
H1 = entropy(rowSums(y2d))
H2 = entropy(colSums(y2d))
H1+H2-H12 # mutual entropyPlease choose more modern alternatives, such as Google Chrome or Mozilla Firefox.