#--------------R code for testing the existence of the first FINITE MOMENT (FINITE MEAN). 
#If you test for a fininte second, third, fourth or k-th moment, raise x to the power of 2, 3, 4 or k.

# H0: the first moment is finite, H1: the moment is not finite (Not necessarily infinite, it can be undefined)
# Cite as Fedotenkov I., (2013) A bootstrap method to test for the existence of finite moments. Journal of Nonparametric Statistics 25(2), p. 315-322.



#--------------------------------------------------------------------   #Input: sample as a vector

tail<-function(x){       

x<-as.vector(x)               #Make a vector, if x is in another format
xi<-0.999                     # Xi, as in the paper
n<-length(x)                  #Number of observations
nn<-max(round(0.4*log(n)),2)  # Size of bootstrap subsamples as in the paper. Minimal size of the subsample is equal to 2.
B<-100000                     #Number of bootstrap subsamples

y<-sample(x, B*nn, replace = TRUE)

Y<-matrix(y,nrow = B,ncol = nn)

mu_star<-apply(matrix(Y,nrow = B,ncol = nn),1,mean)
MU<-mean(x)

MM<-as.numeric(mu_star>xi*MU)

cat("p-value: ") #p-value
mean(MM)
}


#----------------------------------------------------------------------   #EXAMPLE


x<-abs(rcauchy(100000))    #Test works only for positive numbers
 
tail(x)