| criterion {convco} | R Documentation |
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.
criterion(data,epsilon=0.05,mode="p",r=1)
data |
matrix containing the sample paths. |
epsilon |
a numeric value giving the interval endpoint. |
mode |
a character string specifying the mode of convergence to investigate, 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. |
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 rely on
the frequentist approach.
crit |
the vector of criterion values. |
P. Lafaye de Micheaux and B. Liquet
Lafaye de Micheaux, P. (plafaye@club.fr), Liquet, B. "Understanding Convergence Concepts: a Visual-Minded and Graphical Simulation Based Approach", The American Statistician , submitted.
check.convergence, generate, investigate,
law.plot2d, law.plot3d,
p.as.plot, visualize.crit, visualize.sp
myrbinom<-function(n,alpha){rbinom(n,1,1/(1:n))*((1:n)**alpha)}
data <- generate(nmax=1000,M=500,myrbinom,args=list(alpha=0.4))$data
critr1 <- criterion(data,epsilon=0.05,mode="r",r=1)$crit