uniformization: Uniformization
In zhicongz/AnomDetct: Anomaly Detection via Scan Statistics

Description Usage Arguments Details Value Author(s) Examples

This function converts discrete random variables into continuous pseudorandom variables or deals with duplicated case in continuous random variables.

1	unif(x, unit = 1, rd = T)

`x`	a numeric vector of data values.
`unit`	a number indicating the uniformization bin width.
`rd`	logcial; if TRUE, uniformization is done by generating uniform distributed random variable. Otherwise, uniformization is done by evenly cut the unit.

As the sample size getting larger and larger, it is easier to obtain duplicated continuous random variables in the dataset. There is a subtle contradiction invoked in this case because for continuous random variable,

P[x_1=x_2]=0

This function adds residuals on original dataset to avoid duplicated cases. It is an important step for cleaning the data for continuous variables order statistics.
As the unit setted appropriately, the target continuous density function is approximated by sequence of side by side rectangles. This is somehow similar as Cauchy integral.

A sorted numeric vector of length length(x) is returned.
Function will be stopped when unit ≤ 0 .

Zhicong Zhao

x <- rep(c(0.5,1,2), each = 2)

## Uniformization with unit 1 ##
y <- unif(x)
plot(y)

## Uniformization with unit 0.5 ##
y <- unif(x, unit = 0.5)
plot(y)