boot.mean.ml {FuzzySTs}

Estimates the bootstrap distribution of the likelihood ratio LR by the Algorithm 1 or 2 using the mean

Description

Estimates the bootstrap distribution of the likelihood ratio LR by the Algorithm 1 or 2 using the mean

Usage

boot.mean.ml(
  data.fuzzified,
  algorithm,
  distribution,
  sig,
  nsim = 100,
  mu = NA,
  sigma = NA,
  step = 0.1,
  margin = c(5, 5),
  breakpoints = 100,
  plot = TRUE
)

Arguments

data.fuzzified

a fuzzification matrix constructed by a call to the function FUZZ or the function GFUZZ, or a similar matrix. No NA are allowed.

algorithm

an algorithm chosen between "algo1" or "algo2".

distribution

a distribution chosen between "normal", "poisson", "Student" or "Logistic".

sig

a numerical value representing the significance level of the test.

nsim

an integer giving the number of replications needed in the bootstrap procedure. It is set to 100 by default.

mu

if the mean of the normal distribution is known, mu should be a numerical value. Otherwise, the argument mu is fixed to NA.

sigma

if the standard deviation of the normal distribution is known, sigma should be a numerical value. Otherwise, the argument sigma is fixed to NA.

step

a numerical value fixed to 0.1, defining the step of iterations on the interval [t-5; t+5].

margin

an optional numerical couple of values fixed to [5; 5], representing the range of calculations around the parameter t.

breakpoints

a positive arbitrary integer representing the number of breaks chosen to build the numerical alpha-cuts. It is fixed to 100 by default.

plot

fixed by default to "FALSE". plot="FALSE" if a plot of the fuzzy number is not required.

Value

Returns a vector of decimals representing the bootstrap distribution of LR.

Examples

mat <- matrix(c(1,2,2,2,2,1),ncol=1)
MF111 <- TrapezoidalFuzzyNumber(0,1,1,2)
MF112 <- TrapezoidalFuzzyNumber(1,2,2,3)
PA11 <- c(1,2)
data.fuzzified <- FUZZ(mat,mi=1,si=1,PA=PA11) 
emp.dist <- boot.mean.ml(data.fuzzified, algorithm = "algo1", distribution = "normal",
 sig = 0.05, nsim = 5, sigma = 1)
eta.boot <- quantile(emp.dist,  probs = 95/100)