How draw a number from a given vector of distribution?

[Demetrio Guzzardi]

Hello everyone, and happy new year!

I searched everywhere for an answer but could not find any, so I hope someone here could help me out.

I have a vector where each entry is a given probability from 0 to 1.

What I need is a function/way to create a new dummy vector with values 0 or 1 where the probability of having a 1 is given by the probability of the line of the other vector.
That is: if in probability-vector I have an entry with 0.5 I need to have a corresponding cell equal to 1 (almost) half of the time over 100 repetitions of this function.
Something like the table below

Probability	iter1	iter2	iter3	iter4	iter5	iter6	iter7	iter8	iter9	iter10
0.5	1	1	0	1	0	0	1	1	0	1
1	1	1	1	1	1	1	1	1	1	1

Do you know how I could achieve something like this?

please let me know if the question is not clear enough
Thank you all,
D.

[William Lisowski]

Perhaps this example using Mata vectors will start you in a useful direction.

set seed 42
mata:
p1 = .5
p2 = 1
x = runiform(1,10)
y = x:<=p1
z = x:<=p2
x \ y \ z
end

: x \ y \ z
                 1             2             3             4             5             6
    +-------------------------------------------------------------------------------------
  1 |   .755155533   .6390313939   .7521452007   .1362726836   .9032689664   .0940683118
  2 |            0             0             0             1             0             1
  3 |            1             1             1             1             1             1
    +-------------------------------------------------------------------------------------
                 7             8             9            10
     ---------------------------------------------------------+
  1    .5745703041   .3728876995   .2738741017   .3902708814  |
  2              0             1             1             1  |
  3              1             1             1             1  |
     ---------------------------------------------------------+

If not, your question really isn't clear without more detail, or at a minimum it is too difficult to guess at a good answer from what you have shared. Please help us help you. Show example data - your "probability vector". Is it a Stata dataset variable? Is it a Stata matrix? Is it a Mata matrix? In my example, I have just used two Mata scalars for convenience to demonstrate a technique you should be able to adapt.

The Statalist FAQ provides advice on effectively posing your questions, posting data, and sharing Stata output.

[Demetrio Guzzardi]

Thanks a lot William and sorry for not being very clear.

So what I actually did is estimating a probit model from which I estimated the following probabilities in a standard Stata dataset variable (not mata):

* Example generated by -dataex-. To install: ssc install dataex
clear
input double phat_af
    .94836003308945
  .8769213812682086
  .9215910212697133
  .9160083252126953
  .8136632295801208
  .6240468606644965
  .5985503567780064
 .49904546967474017
  .9675509892934736
  .9489425567744427
  .9239985676019286
  .9951993575259833
  .5700241203161944
  .8838109343484395
  .7709431776265225
  .8589910480484257
  .6265504674642524
  .5553053201189672
.032334087049388546
   .974324634276116
end

Now I would like to create a new variable called dummy made of 0 and 1. And the 0 and 1 have to be given by the probability of the variable phat_af. So If I create the 10 dummy, I expect to have Zeros 5 times when the phat_af is equal to 0.5.


Your suggetion is interesting though. Let me see if I got it correctly, you use the uniform distribution to create a new variable that we can call r_unif and compare the phat_af with r_unif. If r_unif<=phat_af then the dummy is equal to 1, and 0 otherwise. Is that what you meant right?

But, and this is of course my limitation, in this way am I actually drawing from the probability phat_af? I am not sure if it is statistically the same


Thank you a lot in any case for your time.
D.

[Mike Lacy]

Thanks for clarifying that your question involved numbers stored in a variable, not in a vector.

So, relying on: "create a new variable ...[with] 0 and 1 ... given by the probability of the variable phat_a."

gen byte y = (runiform() < phat_a)

[William Lisowski]

in this way am I actually drawing from the probability phat_af? I am not sure if it is statistically the same

If we follow the code in post #4 to generate the variable y, then Pr{y=1} = Pr{runiform()<phat_af} = F(phat_af) where F is the cumulative distribution function of a uniform(0,1) random variable.

But F(x) = x defines the cumulative distribution function of a uniform(0,1) random variable, so F(phat_af) = phat_af.

Thus Pr{y=1} = phat_af, which is what you seek.

[Demetrio Guzzardi]

That's great.
Thank you Mike for this very neat code and thank you William for your explanations.

Have an happy new year!