       RE:

• To: mathgroup at smc.vnet.net
• Subject: [mg23343] RE:[mg23270]
• From: "Higinio Ramos Calle" <higra at gugu.usal.es>
• Date: Thu, 4 May 2000 02:59:11 -0400 (EDT)
• Sender: owner-wri-mathgroup at wolfram.com

```----- Original Message -----
From: <com3 at ix.netcom*NOSPAM*.com>
To: mathgroup at smc.vnet.net
Subject: [mg23343] [mg23270] Generating Random Values with Do[]

> Hi,
>
> I'm just at the beginning level of Mathematica programming and I need
> to simulate a probabilistic process. I've constructed the code below
> which (I believe) works fairly well. The intent is to compute the
> number of times a randomly sampled value from distribution #1 will
> equal or exceed a random sample from distribution #2 when a million
> samples from each are compared. This is then repeated  3 times . I've
> used ver. 3.0 for this.  I have 3 questions though.
>
> 1) How can I enhance this code such that I can easily change the
> number of repeats, say from 3 to 10 without copying and pasting the
> code ? Can this be done via an outer Do command ?
>
> 2) Because a million samples from the two distributions are being
> produced and compared, execution time is becoming an issue. Is there a
> way I can speed up this code ?
>
> 3) I understand that the random number generation seed is determined
> from the system date. Could I be getting sub-quality random number
> generation in my code ? In other words, do I need to worry about
> "re-seeding" each time I call Random ?
>
> To get instant execution of the code, you can change the 10^6 to 10^2.
>
> Thanks in advance for any help suitable for the beginner.
>
> Steve
>
>
> Needs["Statistics`NormalDistribution`"]
> Remove["`*"]
> counter={};
> count=0;
> dist1=NormalDistribution[0,1];
> dist2=NormalDistribution[0,1];
> Do[If[Random[dist1] \[GreaterEqual] Random[dist2], count = count +
1,
> count = count], {10^6}]
> counter=Append[counter,count]
> count=0
> Do[If[Random[dist1] \[GreaterEqual] Random[dist2], count = count +
1,
> count = count], {10^6}]
> counter=Append[counter,count]
> count=0
> Do[If[Random[dist1] \[GreaterEqual] Random[dist2], count = count +
1,
> count = count], {10^6}]
> counter=Append[counter,count]

Here is a posible response

Needs["Statistics`NormalDistribution`"]
Remove["`*"]
counter={};
timesYouDo[n_]:=Module[{count,dist1,dist2},
dist1=NormalDistribution[0,1];
dist2=NormalDistribution[0,1];
Do[count=0;
Do[If[Random[dist1] \[GreaterEqual] Random[dist2], count = count
+ 1,
count = count], {10^2}];
counter=Append[counter,count],{n}];counter]

where in n you put the times you want to repeat the task.

Higinio Ramos