discretize {entropy} R Documentation

## Discretize Continuous Random Variables

### Description

`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.

### Usage

```discretize( x, numBins, r=range(x) )
discretize2d( x1, x2, numBins1, numBins2, r1=range(x1), r2=range(x2) )
```

### Arguments

 `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).

### Details

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.

### Value

`discretize` returns a vector containing the counts for each bin.

`discretize2d` returns a matrix containing the counts for each bin.

### Author(s)

Korbinian Strimmer (http://www.strimmerlab.org).

`entropy`.

### Examples

```# 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 entropy

```

[Package entropy version 1.3.0 Index]