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
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 , submitted.
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
Results
R version 3.3.1 (2016-06-21) -- "Bug in Your Hair"
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Platform: x86_64-pc-linux-gnu (64-bit)
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> library(ConvergenceConcepts)
Error in library(ConvergenceConcepts) :
there is no package called 'ConvergenceConcepts'
Execution halted