# Quantile normalization

### Description

Quantile normalizes two vectors or a matrix.

### Usage

1 |

### Arguments

`x` |
Numeric vector or matrix |

`y` |
Optional second numeric vector |

### Details

We sort the columns, take averages across rows, and then plug the averages back into the respective positions. The marginal distributions in the columns are thus forced to be the same. Missing values, which can result in differing numbers of observed values per column, are dealt with by linear interpolation.

### Value

If two vectors, `x`

and `y`

, are provided, the output is a
matrix with two columns, with the quantile normalized versions of
`x`

and `y`

.
If `y`

is missing, `x`

should be a matrix, in which case the
output is a matrix of the same dimensions with the columns quantile
normalized with respect to each other.

### Examples

1 2 3 4 5 6 7 8 9 10 11 12 | ```
z <- rmvn(10000, mu=c(0,5,10), V = rbind(c(1,0.5,0.5),c(0.5,1,0.5),c(0.5,0.5,1)))
z[sample(prod(dim(z)), 1500)] <- NA
pairs(z)
br <- seq(min(z, na.rm=TRUE), max(z, na.rm=TRUE), length=200)
par(mfrow=c(3,1))
for(i in 1:3)
hist(z[,i], xlab="z", main=i, breaks=br)
zn <- normalize(z)
br <- seq(min(zn, na.rm=TRUE), max(zn, na.rm=TRUE), length=200)
for(i in 1:3)
hist(zn[,i], xlab="normalized z", main=i, breaks=br)
pairs(zn)
``` |

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