btestk.mean {SAFD}

Multi-sample bootstrap test for the equality of the mean of FRVs

Description

Given a list XXX of length k sublists of polygonal fuzzy numbers the function first checks if each element of the sublists has the correct format and if the alpha-levels of all input fuzzy numbers coincide. The vector sel contains the numbers of the sublists the user wants to filter to. After filtering the relevant part of XXX the function computes the test-statistic, which compares the sum of the distances of the groups means and the overall mean with the sum of the group variances. Before doing the resampling length(sel) new samples are calculated by adding to each element of every fixed group the sum of all means of the other groups. Based on these length(sel) new samples B values of the (bootstrap) 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 the via sel selected samples from XXX and the total mean are plotted, otherwise no plot is produced. For a more detailed explanation see the papers [1] and [2] below.

Usage

btestk.mean(XXX, sel, theta = 1/3, B = 100, pic = 1)

Arguments

XXX

... A list of sublists, each of which contains polygonal fuzzy numbers

sel

...vector, selection of number of the samples (sublists) to be considered

theta

...numeric and >0

B

...integer, by default B=100.

pic

...numeric, if pic=1 then the sample means of the via sel selected samples from XXX and the total mean are plotted. By default pic=1.

Details

See examples

Value

Given input XXX in the correct format, the function returns the p-value of the two-sided test.

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] Gil, M.A.; Montenegro, M.; Gonzalez-Rodriguez, G.; Colubi, A.; Casals, R.: Bootstrap approach to the multi-sample test of means with imprecise data, Computational Statistics and Data Analysis, 51(1), pp. 148-162 (2006)

See Also

See Also as Mmean, Bvar, bertoluzza, btest1.mean, btest2.mean

Examples

#Example 1: very small B only for testing purpose
data(Trees)
sel<-c(1,2,3)
b<-btestk.mean(Trees,sel,B=5)
b

#Example 2: run for bigger B
#b<-btestk.mean(Trees,sel,100)
#b