# Two-sample bootstrap test on the equality of mean of two FRVs 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. ```r btest2.mean(XX, YY, theta = 1/3, B = 100, pic = 1) ``` ## Arguments - `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. ## Details See examples ## Returns Given input `XX` and `YY` in the correct format, the function returns the p-value of the two-sided bootstrap test. ## References [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) ## Author(s) Wolfgang Trutschnig , Asun Lubiano ## Note 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. ## See Also See Also as `Mmean`, `Bvar`, `bertoluzza`, `btest1.mean`, `btestk.mean` ## Examples ```r #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 ```

btest2.mean function