Global indicator for summarizing the epistemic uncertainty.

Function for summarizing the uncertainty propagation's results in the form of a global indicator corresponding the area between the upper and lower CDFs.

Usage

uncertainty(Z0, disc = 0.01)

Arguments

Z0

Output of the uncertainty propagation function PROPAG().

disc

Integer to specify number of the uniform discretisation of the pair of CDFs. By default, disc=0.01

Value

Value of the area between both CDFs.

Details

Details of the theory and the example in Dubois & Guyonnet (2011) Available at: https://hal-brgm.archives-ouvertes.fr/file/index/docid/578821/filename/Uncertainties_RA_09_l_dg.pdf

See also

propag proba_interval quan_interval

Examples

if (FALSE) {
#################################################
#### EXAMPLE 1 of Dubois & Guyonnet (2011)
#### Probability and Possibility distributions
#################################################

#### Model function
FUN = function(X){
  UER = X[1]
  EF = X[2]
  I = X[3]
  C = X[4]
  ED = X[5]
  return(UER*I*C*EF*ED/(70*70*365))
}

ninput = 5 #Number of input parameters
input = vector(mode = "list", length = ninput) # Initialisation

input[[1]] = create_input(
    name = "UER",
    type = "possi",
    distr = "triangle",
    param = c(2.e-2, 5.7e-2, 1.e-1),
    monoton = "incr"
    )
input[[2]] = create_input(
    name = "EF",
    type = "possi",
    distr = "triangle",
    param = c(200, 250, 350),
    monoton = "incr"
    )
input[[3]] = create_input(
    name = "I",
    type = "possi",
    distr = "triangle",
    param = c(1, 1.5, 2.5),
    monoton = "incr"
    )
input[[4]] = create_input(
    name = "C",
    type = "proba",
    distr = "triangle",
    param=c(5e-3, 20e-3, 10e-3)
    )
input[[5]] = create_input(
    name = "ED",
    type = "proba",
    distr = "triangle",
    param = c(10, 50, 30)
    )

####CREATION OF THE DISTRIBUTIONS ASSOCIATED TO THE PARAMETERS
input = create_distr(input)

####VISU INPUT
plot_input(input)

#################################################
#### PROPAGATION

#OPTIMZATION CHOICES
choice_opt = NULL #no optimization needed
param_opt = NULL

#PROPAGATION RUN
Z0_IRS = propag(N = 1000, input, FUN, choice_opt, param_opt, mode = "IRS")

#################################################
#### POST-PROCESSING

# VISU - PROPAGATION
plot_cdf(Z0_IRS, xlab = "Z", ylab = "CDF", main = "EX 1", lwd = 1.5)

# interval of quantiles
level = 0.95
quant = quan_interval(Z0_IRS, level)
Qlw = quant$Qlow
Qup = uant$Qupp
print(paste("interval of quantiles at level:",level," : ",
  "Qlow:",round(Qlw/10^floor(log10(Qlw)),
  abs(floor(log10((Qup-Qlw)/10^ceiling(log10(Qlw))))))*10^floor(log10(Qlw)),
  " & Qup:",round(Qup/10^floor(log10(Qup)),
  abs(floor(log10((Qup-Qlw)/10^ceiling(log10(Qup))))))*10^floor(log10(Qup)),sep="")
  )

# interval of probabilities
thres = 1e-5
prob = proba_interval(Z0_IRS, thres)
print(paste("interval of probabilities at threshold:",thres," : ",
  "Plow:",prob$Plow,
  " & Pup:",round(prob$Pupp,3),sep="")
  )

# Global indicator of uncertainty
unc = uncertainty(Z0_IRS)
print(paste("Epistemic uncertainty : ",unc,sep=""))

}