btest2.mean: Two-sample bootstrap test on the equality of mean of two FRVs
In SAFD: Statistical Analysis of Fuzzy Data

Description Usage Arguments Details Value Note Author(s) References See Also Examples

Given two samples XX and YY of polygonal fuzzy numbers the function first checks if each element of XX and YY has the correct format and if the alpha-levels of all input fuzzy numbers coincide. In case yes, the function compute the test statistic described in [1] below. Before doing the resampling Mmean(YY) is added to each element of XX and vice versa. Based on these two new samples B values of the test statistic are calculate. The returned p-value is calculated as the portion of the obtained values of the bootstrap statistic that are greater than the value of the test-statistic. If pic=1 then the sample means of XX and YY are plotted, otherwise no plot is produced. For detailed explanation see the papers [1] and [2] below.

1	btest2.mean(XX, YY, theta = 1/3, B = 100, pic = 1)

`XX`	...should be a list of polygonal fuzzy numbers (the functions implicitly checks the conditions)
`YY`	...should be a list of polygonal fuzzy numbers (the functions implicitly checks the conditions)
`theta`	...numeric and >0
`B`	...integer, by default `B`=1000.
`pic`	...numeric, if `pic`=1 then the sample means of `XX` and `YY` are plotted. By default `pic`=1.

See examples

Given input XX and YY in the correct format, the function returns the p-value of the two-sided bootstrap test.

The function is quite slow.
In case you find (almost surely existing) bugs or have recommendations for improving the functions comments are welcome to the above mentioned mail addresses.

Wolfgang Trutschnig <wolfgang@trutschnig.net>, Asun Lubiano <lubiano@uniovi.es>

[1] Colubi, A.: Statistical inference about the means of fuzzy random variables: Applications to the analysis of fuzzy- and real-valued data, Fuzzy Sets and Systems, 160(3), pp. 344-356 (2009)

[2] Montenegro, M., Casals, M.R., Lubiano, M.A., Gil, M.A.: Two-sample hypothesis tests of means of a fuzzy random variable, Information Sciences, Vol. 133(1-2), pp. 89-100 (2001)

See Also as Mmean, Bvar, bertoluzza, btest1.mean, btestk.mean

#Example 1: run for bigger B
data(XX)
X<-translator(XX[[1]],20)
Y<-translator(XX[[2]],20)
XX<-vector("list",length=30)
for (j in 1:30){
 XX[[j]]<-generator(X,)
 }
YY<-vector("list",length=20)
for (j in 1:20){
 YY[[j]]<-generator(Y,)
 }
b<-btest2.mean(XX,YY,B=10)
b

#Example 2: takes some time in the current version:
#data(Trees)
#b<-btest2.mean(Trees[[1]],Trees[[2]],50)
#b
#b<-btest2.mean(Trees[[1]],Trees[[3]],50)
#b