SAFD (version 2.1)

btest1.mean: One-sample bootstrap test for the mean of a FRV

Description

Given a sample XX of polygonal fuzzy numbers and a polygonal fuzzy number V the function first checks if each element of XX and V has the correct format and if the alpha-levels of all input fuzzy numbers coincide. In case yes, the function computes the standardized mean squared Bertoluzza-distance from the sample mean to V as test-statistic. Afterwards for B bootstrap samples the (bootstrap) statistic is calculated. 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. Furthermore, if pic=1 sample mean and V are plotted. For detailed explanation see papers [1] and [2] below.

Usage

btest1.mean(XX, V, theta = 1/3, B = 100, pic = 0)

Arguments

XX

...list of polygonal fuzzy numbers (the functions implicitly checks the conditions).

V

...polygonal fuzzy number that is tested to be the mean of the FRV.

theta

...numeric and >0, see bertoluzza

B

...integer, by default B=1000.

pic

...numeric, if pic=1 sample mean and V are plotted. By default pic=1.

Value

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

Details

See examples

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., Colubi, A., Casals, M.R., Gil, M.A.: Asymptotic and bootstrap techniques for testing the expected value of a fuzzy random variable, Metrika, 59, pp. 31-49 (2004)

See Also

See Also as Mmean, Bvar, bertoluzza, btest2.mean, btestk.mean

Examples

# NOT RUN {
#Example 1: run for bigger sample sizes:
data(XX)
V<-translator(XX[[3]],50)
V2<-V
SS<-vector("list",length=50)
for (j in 1:50){
 SS[[j]]<-generator(V2,)
 }
b<-btest1.mean(SS,V2,B=10)
b

#Example 2: takes some time to run:
#data(Trees)
#V<-Trees[[1]][[47]]
#b<-btest1.mean(Trees[[1]],V,100)
#b
# }