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Type of input variables (imprecise, random or fixed).

create_input.Rd

Function to define the type of input variables (imprecise, random or fixed). Five types are accounted for:

  • Probability distribution (either pre-defined (Normal, log-Normal, uniform, triangular, Beta) or user-defined).

  • Possibility distribution (either trapezoidal or triangular).

  • Intervals.

  • Fixed scalar value.

  • Imprecise probability distributions (Normal, log-Normal, uniform, triangular, Beta) with parameters represented by by intervals, possibility distributions, fixed scalar values, or probability distributions.

Usage

create_input(name, type, distr = NULL, param, 
    monoton = "dunno", quser = NULL, ruser = NULL)

Arguments

name

String of the name of the input variable.

type

String to specify the type of input variable:

  • "proba": probability distribution.

  • "possi": possibility distribution.

  • "impr proba": imprecise probability distribution

  • "fixed": fixed scalar value.

distr

String to specify the type of distribution:

  • If type="proba" or type="impr proba", distr should be: "normal", "lognormal","uniform", "triangle", "beta","user".

  • If type="possi", distr should be: "trapeze", "triangle", "interval".

param

Vector of parameter values. This depends on the choice of distr and type.

  • If type="proba" and distr="normal", param should be a vector of two values. For example c(0,1) corresponds to a normal distribution with mean=0 and standard deviation of 1.

  • If type="proba" and distr="lognormal", param should be a vector of two values. For example c(0,1) corresponds to a lognormal distribution with meanlog=0 and standard deviation of sdlog=1.

  • If type="proba" and distr="uniform", param should be a vector of two values. For example c(0,1) corresponds to a uniform distribution with support[0,1].

  • If type="proba" and distr="triangle", param should be a vector of three values. For example c(0,2,1) corresponds to a triangle distribution with apex=1 and support[0,2]. See help from package triangle.

  • If type="proba" and distr="beta", param should be a vector of two values. For example c(1,1) corresponds to a beta distribution with parameters shape1 and shape2 equal to 1 (see help of qbeta in stats package).

  • If type="possi" and distr="trapeze", param should be a vector of four values. For example c(0,1,2,3) corresponds to a possibility distribution with core=[1,2] and support=[0,3].

  • If type="possi" and distr="triangle", param should be a vector of three values. For example c(0,1,2) corresponds to a possibility distribution with core=1 and support=[0,2].

  • If type="possi" and distr="interval", param should be a vector of two values. For example c(0,1) corresponds to the interval [0,1].

  • If type="impr proba", param should be a vector of integers; each integer points to the rank of the input, which represents the uncertainty on the corresponding parameter of chosen distribution For example, if type="impr proba" and distr="normal", c(2,3) corresponds to an imprecise normal distribution, whose imprecise mean is input[[2]] and standard deviation is input[[3]].

monoton

String to specify the monotony of the model function regarding the input variable.

  • "decr" for decreasing.

  • "incr" for increasing.

  • "dunno" for unknown monotony or known no-monotony.

quser

If distr="user", this string specifies the quantile function of a probability distribution non listed in the pre-defined ones. The vector of param should be updated according to this law.

ruser

If distr="user", string to specify the random sampling function of a probability distribution non listed in the pre-defined ones. The vector of param should be updated according to this law.

Value

list with the afore-described arguments.

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

create_distr plot_input

Examples


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

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)
    )
    
#################################################
#### EXAMPLE 2 of Sch\"obi & Sudret (2016)
#### Imprecise Probability distributions
#################################################

ninput <- 6 #Number of input parameters
input<-vector(mode="list", length=ninput) # Initialisation

# Imprecise normal probability 
# whose parameters are described by the 3rd and 5th parameters
input[[1]] = create_input(
    name="A",
    type="impr proba",
    distr="normal",
    param=c(3, 5),
    monoton="dunno"
    )

# Imprecise normal probability
# whose parameters are described by the 4th and 6th parameters
input[[2]] = create_input(
    name="B",
    type="impr proba",
    distr="normal",
    param=c(4, 6),
    monoton="dunno"
    )

# imprecise paramters of afore-described probability distribution
# mean of input number 1 as an interval
input[[3]] = create_input(
    name="mu_A",
    type="possi",
    distr="interval",
    param=c(-0.5, 0.5)
    )

# mean of input number 2 as an interval
input[[4]] = create_input(
    name="mu_B",
    type="possi",
    distr="interval",
    param=c(-0.5, 0.5)
    )

# standard deviation of input number 1  as an interval
input[[5]] = create_input(
    name="s_A",
    type="possi",
    distr="interval",
    param=c(0.7, 1)
    )

# standard deviation of input number 2  as an interval
input[[6]] = create_input(
    name="s_B",
    type="possi",
    distr="interval",
    param=c(0.7, 1)
    )