# boot.mean.ml: Estimates the bootstrap distribution of the likelihood ratio... In FuzzySTs: Fuzzy Statistical Tools

## Description

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

## Usage

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13``` ```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

 ```1 2 3 4 5 6 7 8``` ```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) ```

FuzzySTs documentation built on July 8, 2020, 7:17 p.m.