random number generator plus controlled sum constraint

[Liu Qiang]

Dear all,
In my project, Monte Carlo simulation is applied. But I have to control the sum of the observations as a constant while using a rnd command. For example, I want to generate an X~N(40, theta2) and set the observation number at 100. The sum then can be estimated as 4000. But using

 gen x= 40+invnormal(uniform())

can only ensure the sum close to 4000 but cannot make sure exactly equal to 4000. Does anyone knows how to reach this goal?

[Andrew Musau]

My brute force approach from #9 in this link will give you an option of seeds.

*OVER 1000 TRIALS, EXTRACT SEED
set obs 100
forvalues i= 1/1000{
gen seed`i'="`c(seed)'"
gen x`i'= 40+invnormal(uniform())
egen totalx`i'= total(x`i')
}

keep in 1
*ssc install fastreshape
keep seed* totalx*
gen n=1
fastreshape long seed totalx, i(n)

*BROWSE OBSERVATIONS WHICH SUM TO 4000
sort totalx
browse if inrange(totalx,3999.99, 4000.10)

*SELECT APPROPRIATE SEED, e.g., in OBS. No. 523 for me
local seed = seed in 523

*USE SEED
clear
set obs 100
set seed `seed'
gen x= 40+invnormal(uniform())
egen totalx= total(x)
list totalx in 1

. set seed `seed'

.
. gen x= 40+invnormal(uniform())

.
. egen totalx= total(x)

.
. list totalx in 1

     +----------+
     |   totalx |
     |----------|
  1. | 4000.048 |
     +----------+

[Scott Merryman]

Take a look corr2data

. corr2data x, m(40) sd(1) n(100) double
(obs 100)

. sum

    Variable |        Obs        Mean    Std. Dev.       Min        Max
-------------+---------------------------------------------------------
           x |        100          40           1   37.64696   42.03049