btest1.mean {SAFD}

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.

Details

See examples

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.

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.

Author(s)

Wolfgang Trutschnig <[e-mail]>, Asun Lubiano <[e-mail]>

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

#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