estimateHellingerDiv {MethylIT} R Documentation

## Hellinger divergence of methylation levels

### Description

Given a the methylation levels of two individual, the function computes the information divergence between methylation levels.

### Usage

```estimateHellingerDiv(p, n = NULL)
```

### Arguments

 `p` A numerical vector of the methylation levels p = c(p1, p2) of individuals 1 and 2. `n` if supplied, it is a vector of integers denoting the coverages used in the estimation of the methylation levels.

### Details

Each methylation level j for cytosine site i corresponds to a probability vector p_j = c(p_ij, 1 - p_ij). Then, the information divergence between methylation levels p1 and p2 is the divergence between the vectors p1 = c(p_i1, 1 - p_i1) and p2 = c(p_i2, 1 - p_i2). If the vector of coverage is supplied, then the information divergence is estimated according to the formula:

hdiv = 2*(n + 1)*(n + 1)*((sqrt(p) - sqrt(p))^2 + (sqrt(1 - p) - sqrt(1 - p))^2)/(n + n + 2) This formula corresponds to Hellinger divergence as given in the first formula from Theorem 1 from reference 1. Otherwise: hdiv = (sqrt(p) - sqrt(p))^2 + (sqrt(1 - p) - sqrt(1 - p))^2

### Value

The Hellinger divergence value for the given methylation levels is returned

### References

' 1. Basu A., Mandal A., Pardo L (2010) Hypothesis testing for two discrete populations based on the Hellinger distance. Stat Probab Lett 80: 206-214.

### Examples

```    p <- c(0.5, 0.5)
estimateHellingerDiv(p)

```

[Package MethylIT version 0.3.1 ]