Description Usage Arguments Details Value Author(s) References Examples
Estimate a failure probability by MRM method.
1 |
f |
a failure fonction |
inputDimension |
dimension of the inputs |
inputDistribution |
a list of length ‘inputDimension’ which contains the name of the input distribution and their parameters. For the input "i", inputDistribution[[i]] = list("name_law",c(parameters1,..., parametersN)) |
dir.monot |
vector of size |
N.calls |
Number of calls to f allowed |
Method |
there is two methods available. "MC" is an adapation of the Monte Carlo method under constraints of monotony. "MRM" is based on a sequential sampling. |
silent |
if silent = TRUE, print curent number of call to f. Default: FALSE. |
These methods compute the probability that the output of the failure function is negative
Um |
Exact lower bounds of the failure probability |
UM |
Exact upper bounds of the failure probability |
MLE |
Maximum likelihood estimator of the failure probability |
IC.inf |
Lower bound of the confidence interval of the failure probability based on MLE |
IC.sup |
Upper bound of the confidence interval of the failure probability based on MLE |
CV.MLE |
Coefficient of variation of the MLE |
X |
design of experiments |
Y |
value of f on X |
N.tot |
Total number of simulation (only for "MC_monotone") |
Vincent Moutoussamy and Nicolas Bousquet
Bousquet, N. (2012) Accelerated monte carlo estimation of exceedance probabilities under monotonicity constraints. Annales de la Faculte des Sciences de Toulouse. XXI(3), 557-592.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 | ## Not run:
inputDistribution <- list()
inputDistribution[[1]] <- list("norm",c(4,1))
inputDistribution[[2]] <- list("norm",c(0,1))
inputDistribution[[3]] <- list("norm",c(-1,3))
inputDimension <- length(inputDistribution)
p <- 1e-5
threshold <- qnorm(p, 3, sqrt(11))
f <- function(Input){
sum(Input) - threshold
}
dir.monot <- c(1, 1, 1)
N.calls <- 300
res.MRM <- MRM(f, inputDimension, inputDistribution,
dir.monot, N.calls, Method = "MRM", silent = FALSE)
N <- 1:dim(res.MRM[[1]])[1]
plot(N, res.MRM[[1]][, 1],
col = "black", lwd=2, type='l', ylim=c(0, 50*p),
xlab="Number of runs to the failure function",
ylab="")
lines(N, res.MRM[[1]][, 2], col = "black", lwd = 2)
lines(N, res.MRM[[1]][, 3], col = "red", lwd = 2)
lines(N, res.MRM[[1]][, 7], col = "blue", lwd = 2, lty = 2)
lines(N, rep(p, length(N)), lwd= 2, col= "orange", lty=3 )
legend("topright",
c("Exact Bounds", "MLE","p.hat", "p"),
col = c("black", "red", "blue", "orange"),
text.col = c("black", "red", "blue", "orange"),
lty = c(1, 1, 2, 3),
merge = TRUE)
## End(Not run)
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