# criterion: Convergence criterion computation In ConvergenceConcepts: Seeing Convergence Concepts in Action

## Description

This function computes the values of the criterion convergence function for convergence in probability, almost surely or in r-th mean, given the sample paths.

## Usage

 `1` ```criterion(data,epsilon=0.05,mode="p",r=2) ```

## Arguments

 `data` matrix containing the sample paths of Xn-X values. `epsilon` a numeric value giving the interval endpoint. `mode` a character string specifying the mode of convergence to be investigated, must be one of "p" (default), "as" or "r". `r` a numeric value (r>0) if convergence in r-th mean is to be studied.

## Details

The `data` matrix contains the X_n-X values. If mode="p", `criterion` approximates p_n=P[|X_n-X|>ε]. If mode="as", `criterion` approximates a_n=P[it exists k>= n;|X_k-X|>ε]. If mode="r", `criterion` approximates e_{n,r}=E|X_n-X|^r. The approximations are based on the frequentist approach.

## Value

 `crit ` the vector of criterion values.

## Author(s)

P. Lafaye de Micheaux and B. Liquet

## References

Lafaye de Micheaux, P. (plafaye@club.fr), Liquet, B. "Understanding Convergence Concepts: a Visual-Minded and Graphical Simulation Based Approach", The American Statistician, 63:2, 173–178, (2009).

`check.convergence`, `generate`, `investigate`, `law.plot2d`, `law.plot3d`, `p.as.plot`, `visualize.crit`, `visualize.sp`
 ```1 2 3``` ```myrbinom <- function(n,alpha){rbinom(n,1,1/(1:n))*((1:n)**alpha)} data <- generate(nmax=1000,M=500,myrbinom,args=list(alpha=0.5))\$data critr1 <- criterion(data,mode="r",r=1)\$crit ```