write a program in R statistic program, which will simulate the process of n coupon collector(the popular problem)
The program must record the number of the boxes of a product, that someone bought until (s)he collects all the coupons. Do an application for n=15 repeating the process for 1000 times.
If X_i is the number of the boxes which had to be purchased until the 15 coupons to be completed during the i-th iterataion of the process, calculate the average of X_1,,...,X_1000.
Can anyone tell me what the above code does? every command of it!..Is it what I need ?
Here is what I found!
Code:
nbought <- function(N) {
coupons <- matrix(0,1,N) # initially have no coupons
for (k in 1:1000) { # collect until complete collection
x <- sample.int(N, 1, replace = TRUE)
coupons[x] <- 1 # mark that coupon type as collected
ifelse(sum(coupons)==N,return(k),-1)
} }
N <- 15 # set to desired number of different coupons
y <- sapply(matrix(N,100,1),nbought)
average<- mean(y) #added by me
another one :
Code:
Tmax = 1000
coupons = 72
prob = rep(0,Tmax)
prob[1:(coupons - 1)] = 1
prob[coupons:Tmax]= 0
for (T in coupons:Tmax) {
for (k in 1:(coupons - 1)) {
prob[T] = prob[T] + (-1)^(k+1)*choose(coupons,k)*((coupons - k)/coupons)^T
}
}
prob[1:Tmax] = 1 - prob[1:Tmax]
prob
and finally this:
Code:
x<-1:5
if.true<-FALSE
reps<-rep(0,1000)
for (j in 1:1000){
i<-1
repeat{
sample<-sample(x,5,replace=TRUE)
check<-x %in% sample
if.true<-all.equal(check, rep(TRUE,5))
if(if.true==TRUE){break}
i<-i+1
}
reps[j]<-i
}
Coupon collector's problem
http://www.math.uni.wroc.pl/~debicki...lekcjonera.pdf
thanks
