check.convergence {convco} R Documentation

## Check convergence

### Description

This function enables one to investigate the four classical modes of convergence on simulated data: in probability, almost surely, in r-th mean and in law.

### Usage

```check.convergence(nmax,M,genXn,argsXn=NULL,mode="p",epsilon=0.05,r=2,nb.sp=10,density=TRUE,densfunc=dnorm,probfunc=pnorm,tinf=-3,tsup=3,trace=plot)
```

### Arguments

 `nmax` number of points in each sample path. `M` number of sample paths to generate. `mode` a character string specifying the mode of convergence to investigate, must be one of "p" (default), "as", "r" or "L". `genXn` a function that generates the Xn-X values, or only the Xn values in the law case. `argsXn` a list of arguments to `genXn`. `epsilon` a numeric value giving the interval endpoint. `r` a numeric value (r>0) if convergence in r-th mean is to be studied. `nb.sp` number of sample paths to draw on the left plot. `density` if density=TRUE, then the plot of the density of X and the histogram of Xn is returned. If density=FALSE, then the plot of the distribution function F(t) of X and the empirical distribution Fn(t) of Xn is returned. `densfunc` function to compute the density of X. `probfunc` function to compute the distribution function of X. `tinf` lower limit from where you want to investigate convergence in law. `tsup` upper limit to where you want to investigate convergence in law. `trace` type of function used to draw the plot: `plot` or `points`. `...` optional arguments to `trace`.

### Details

The objective of this function is to investigate graphically the convergence of some random variable Xn to some random variable X. In order to use it, you should be able to provide generators of Xn and X (or of Xn-X). The four modes of convergence that you can try are: in probability, almost surely, in r-th mean and in law.

a completer

### 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 , submitted.

`criterion`, `generate`, `investigate`, `law.plot2d`, `law.plot3d`, `p.as.plot`, `visualize.crit`, `visualize.sp`

### Examples

```########### Exercise 1 from the article ###########

pnotasgen<-function(n){
Z<-runif(1)
k<-floor(log2(1:n))
m<-1:n-2^k
res<-(m*2^(-k)<= Z & Z<(m+1)*2^(-k))
return(as.integer(res))
}

check.convergence(nmax=1000,M=500,genXn=pnotasgen,mode="as")

```

[Package convco version 0.4 Index]