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Simulations code

m1 <- vector("list", 100)
library(parallel)
cl <- makeCluster(detectCores())
clusterEvalQ(cl, library(Rpickands))
system.time({
  m1 <- parLapply(cl, 1:100,Take_expected_value, copy_number=100000,points=10000)
})
stopCluster(cl)

user system elapsed

0.22 0.91 2741.93

plot(unlist(m1)/1:100, ylim=c(0,3))
abline(h=1/(sqrt(pi)), col="red")
unlist(m1)

Results:

[1]  2.696103  3.824087  4.757944  5.782585  6.103098  8.314943  7.933611  8.586543  9.239043 11.644069 10.191150 12.010007
[13] 16.825036 14.475594 13.182947 14.777401 10.451305 23.840736 14.237660  9.955883 17.517705 19.271054 14.542429 12.563869
[25] 11.377340 10.100034 19.189640 12.080305 14.395206 22.932530 11.070851 75.039759 10.139179 28.693873 10.352961 14.428169
[37] 10.980427 13.175679 18.998276 10.090254 10.091116 13.606485 12.646165 12.196682 15.277995 10.864889 10.761174 12.558026
[49] 11.161201 21.001675  9.187723 20.033081  8.636519 26.310541 67.970616 10.430356 10.746864 14.495912 19.766499 12.845559
[61] 11.045934 11.820578 10.737559 11.564290 13.168917 10.964343 16.186598 17.438162 13.712377 24.905167 22.606472  9.789053
[73] 16.089995 11.796208 23.471996 10.010266 12.803666 10.331008 19.545839 14.429806 80.925815 10.553487 20.343777 19.146669
[85] 14.432933 10.713293  9.557530  9.406336 12.601006 10.623573 59.562875 10.918457 14.719750 14.125113 10.156976 10.098214
[97] 10.500530 10.508240 14.317996 14.265341

Plot of results -> unlist(m1)/1:100

rplot01

Some time elapsed of generating from rnorm

Code

library(parallel)
 cl <- makeCluster(detectCores())
 clusterEvalQ(cl, library(Rpickands))

 system.time({
    ma <- rnorm(10^9)
 })
 stopCluster(cl)

Time:

 user  system elapsed 
 70.68    2.80   77.47 

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