[R] "rbinom" : Does randomness preclude precision?

[Charles Annis, P.E.]

I think I see the rub:  You would like to see the distribution of a sample
be identical to the distribution from which it was sampled.  But if it is
random then that can happen only in the long run, not on every sample.  That
is why samples from a normal density are *not* themselves normal - they're
"t."  When the sample size is large enough the differences between a random
sample's density and its parent density become vanishingly small.  Thus the
differences you observe from repeated random samples from the binomial.
Repeated sampling produces slightly different numbers of successes.  How
could it be otherwise?

Charles Annis, P.E.

Charles.Annis at StatisticalEngineering.com
phone: 561-352-9699
eFax:  614-455-3265
http://www.StatisticalEngineering.com
 
________________________________________
From: Philip Twumasi-Ankrah [mailto:nana_kwadwo_derkyi at yahoo.com] 
Sent: Wednesday, May 28, 2008 10:36 AM
To: Charles.Annis at StatisticalEngineering.com
Subject: RE: [R] "rbinom" : Does randomness preclude precision?

Charles,
When you simulate data from a distribution, what you effect are doing is
generating a sequence of values that would correspond to that distribution.
So you can generate 1000 values from a normal distribution and expect that
when you check on the distribution of your sample (what you do with your
qqnorm or Q-Q plot), it should be a close fit with the theoretical
distribution with the assigned parameter values. It will be difficult to
explain why a simulated data may be different from the distribution it is
was generated from . I think you can not blame it on randomness. 

I hope you understand what I am trying to determine.

"Charles Annis, P.E." <Charles.Annis at StatisticalEngineering.com> wrote:
What do you mean by "... *eventual* nature of the distribution?" If you
simulated 100 samples, would you expect to see 1.5 successes? Or 1? Or 2?
How many, in your thinking, is "eventual?"



Charles Annis, P.E.

Charles.Annis at StatisticalEngineering.com
phone: 561-352-9699
eFax: 614-455-3265
http://www.StatisticalEngineering.com


-----Original Message-----
From: r-help-bounces at r-project.org [mailto:r-help-bounces at r-project.org] On
Behalf Of Philip Twumasi-Ankrah
Sent: Wednesday, May 28, 2008 9:52 AM
To: ted.harding at manchester.ac.uk
Cc: r-help at r-project.org
Subject: Re: [R] "rbinom" : Does randomness preclude precision?

Teds reply is a bit comforting and as indicated in my post, I am resorting
to using "sample" but as an academic issue, does randomness preclude
precision? 

Randomness should be in the sequence of zeros and ones and how they are
simulated at each iteration of the process but not in the eventual nature of
the distribution. 

I mean if I simulated a Normal (0, 1) and got a Normal(1.5, 2) these would
be very different distributions. It is the same with simulating a
Binomial(1, p=0.15) and getting Binomial(1, 0.154)

Ted.Harding at manchester.ac.uk wrote: On 28-May-08 12:53:26, Philip
Twumasi-Ankrah wrote:
> I am trying to simulate a series of ones and zeros (1 or 0) and I am
> using "rbinom" but realizing that the number of successes expected is
> not accurate. Any advice out there.
> 
> This is the example:
> 
> N<-500
> status<-rbinom(N, 1, prob = 0.15)
> count<-sum(status)
> 
> 15 percent of 500 should be 75 but what I obtain from the "count"
> variable is 77 that gives the probability of success to be 0.154. Not
> very good.

The difference (77 - 75 =2) is well within the likely sampling
variation when 500 values are sampled independently with
P(1)=0.15:

The standard deviation of the resulting number of 1s is
sqrt(500*0.15*0.85) = 7.98, so the difference of 2 is only 1/4 of
a standard deviation, hence very likely to be equalled or exceeded.

Your chance of getting exactly 75 by this method is quite small:

dbinom(75,500,0.15)
[1] 0.04990852

and your chance of being 2 or more off your target is

1 - sum(dbinom((74:76),500,0.15))
[1] 0.8510483

> Is there another way beyond using "sample" and "rep" together?

It looks as though you are seeking to obtain exactly 75 1s,
randomly situated, the rest being 0s, so in effect you do need
to do something on the lines of "sample" and "rep". Hence,
something like

status <- rep(0,500)
status[sample((1:500),75,replace=FALSE)] <- 1

Hoping this helps,
Ted.

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Date: 28-May-08 Time: 14:19:24
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