(defun raowu (sch_id num_resam weight_lst g)
"Args: sch_id
Raowu bootstrap: sch_id is a stratified sample of school ids, num_resam is 
the number of resample size. Returns a list of school 
ids which is resampled from the given sample, the number of observations in
 each stratum is proportional to the original stratum size."

; The following program computes the stratum size for the resample.
(let* (
        (l (length sch_id))
        (len_lst (repeat 0 l))
        (len_lst1 (repeat 0 l))
        )
)
   (dotimes (i l)
   (setf (nth i len_lst) (length (nth i sch_id)))
   )
(let* (
        (total (sum len_lst))
       )
)
(dotimes (i l)
   (setf (nth i len_lst1) (round (* (/ (nth i len_lst) total) num_resam)))
)

; The following program gives a list of resample.

(let* (
        (resam nil)
        (mean_lst (repeat 0 l))
       )
)
(dotimes (i l)
   (let* (
           (x (sample (nth i sch_id) (nth i len_lst1) t))
           (resam (append resam (list (copy-list x))))
         )
    )
           (setf (nth i mean_lst) (mean x))

)

; A new sample
(let* (
        (ori_mean (repeat 0 l))
      )
)
   (dotimes (i l)
       (setf (nth i ori_mean) (mean (nth i sch_id) ))
   )
(let* ((y_tilde nil)
       (mean_lst nil)))
(dotimes (i l)
   (let* (x(sum (nth i ori_mean) 
                (prod (sqrt (nth i len_lst1)) 
             (^ (- (nth i len_lst) 1) -.5)  (- (nth i resam) (nth i ori_mean))  
                )
             )
         )
         (y_tilde(append y_tilde (list (copy-list x)))
         (mean_lst(append mean_lst (mean x)))
         (t_tilde(g y_tilde))
   )
)
   (setf y_tilde1(prod weight_lst mean_lst))

(setf theta(g y_tilde1))

)