boot.mean.algo1

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

data.fuzzified

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

distribution

a numerical value representing the significance level of the test.

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

nsim

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

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

sigma

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

step

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

margin

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

breakpoints

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

plot

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

The main goal of this package is to present various fuzzy statistical tools. It intends to provide an implementation of the theoretical and empirical approaches presented in the thesis entitled "The signed distance measure in fuzzy statistical analysis. Some theoretical, empirical and programming advances" (Thesis to be published soon. For the theoretical approaches, see Berkachy R. and Donze L. (2019) <doi:10.1007/978-3-030-03368-2_1>. For the empirical approaches, see Berkachy R. and Donze L. (2016) <ISBN: 978-989-758-201-1>). Important (non-exhaustive) implementation highlights of this package are as follows: (1) a numerical procedure to estimate the fuzzy difference and the fuzzy square. (2) two numerical methods of fuzzification. (3) a function performing different possibilities of distances, including the signed distance and the generalized signed distance for instance. (4) numerical estimations of fuzzy statistical measures such as the variance, the moment, etc. (5) two methods of estimation of the bootstrap distribution of the likelihood ratio in the fuzzy context. (6) an estimation of a fuzzy confidence interval by the likelihood ratio method. (7) testing fuzzy hypotheses and/or fuzzy data by fuzzy confidence intervals in the Kwakernaak - Kruse and Meyer sense. (8) a general method to estimate the fuzzy p-value with fuzzy hypotheses and/or fuzzy data. (9) a method of estimation of global and individual evaluations of linguistic questionnaires. (10) numerical estimations of multi-ways analysis of variance models in the fuzzy context. The unbalance in the considered designs are also foreseen.

Redina Berkachy

FuzzySTs

Fuzzy Statistical Tools

boot.mean.algo1 function

<dl><dt>data.fuzzified</dt>
<dd>a fuzzification matrix constructed by a call to the function FUZZ or the function GFUZZ, 
or a similar matrix. No NA are allowed.</dd>
<dt>distribution</dt>
<dd>a distribution chosen between "normal", "poisson", "Student" or "Logistic".</dd>
<dt>sig</dt>
<dd>a numerical value representing the significance level of the test.</dd>
<dt>nsim</dt>
<dd>an integer giving the number of replications needed in the bootstrap procedure. It is set to 100 by default.</dd>
<dt>mu</dt>
<dd>if the mean of the normal distribution is known, mu should be a numerical value. Otherwise, the argument mu is fixed to NA.</dd>
<dt>sigma</dt>
<dd>if the standard deviation of the normal distribution is known, sigma should be a numerical value. Otherwise, the argument sigma is fixed to NA.</dd>
<dt>step</dt>
<dd>a numerical value fixed to 0.1, defining the step of iterations on the interval [t-5; t+5].</dd>
<dt>margin</dt>
<dd>an optional numerical couple of values fixed to [5; 5], representing the range of calculations around the parameter t.</dd>
<dt>breakpoints</dt>
<dd>a positive arbitrary integer representing the number of breaks chosen to build the numerical alpha-cuts. It is fixed to 100 by default.</dd>
<dt>plot</dt>
<dd>fixed by default to "FALSE". plot="FALSE" if a plot of the fuzzy number is not required.</dd></dl>

Arguments

Estimates the bootstrap distribution of the likelihood ratio LR by the Algorithm 1 using the mean — boot.mean.algo1

<dl>

<dt>data.fuzzified</dt>
<dd>a fuzzification matrix constructed by a call to the function FUZZ or the function GFUZZ, 
or a similar matrix. No NA are allowed.</dd>


<dt>distribution</dt>
<dd>a distribution chosen between "normal", "poisson", "Student" or "Logistic".</dd>


<dt>sig</dt>
<dd>a numerical value representing the significance level of the test.</dd>


<dt>nsim</dt>
<dd>an integer giving the number of replications needed in the bootstrap procedure. It is set to 100 by default.</dd>


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


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


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


<dt>margin</dt>
<dd>an optional numerical couple of values fixed to [5; 5], representing the range of calculations around the parameter t.</dd>


<dt>breakpoints</dt>
<dd>a positive arbitrary integer representing the number of breaks chosen to build the numerical alpha-cuts. It is fixed to 100 by default.</dd>


<dt>plot</dt>
<dd>fixed by default to "FALSE". plot="FALSE" if a plot of the fuzzy number is not required.</dd>

</dl>

boot.mean.algo1: Estimates the bootstrap distribution of the likelihood ratio LR by the Algorithm 1 using the mean

Description

Usage

Value

Arguments