Re: Question for the statisticians

On Jun 28, 5:52 pm, henrysun...@xxxxxxxxx wrote:
So I'm reading "Statistics Demystified" and it states the following
about the Central Limit Theorem:

"According to the first part of the Central Limit Theorem, the
sampling distribution of means is a normal distribution if the
distribution for P is normal.  If the distribution for P is not
normal, then the sample distribution of means approaches a normal
distribution as the sample size N increases.  Even if the distribution
for P is highly sekwed (assymetrical), any sampling distribution of
means is more nearly normal than the distribution of P.  It turns out
that if N>=30, then even if the distribution for P is highly skewed
and P is gigantic, for all practical purposes the sampling
distribution of means is a normal distribution."

I'm curious as to how this might apply (or, alternatively, if it does
not apply) to the issue of bridge simulations.

If one were to run 30 separate 50 hand simulations of the same
problem, would the cumulative result of the simulations tend to be
more close to the theoretical expectancy than running 1 simulation of
1500 trials?

Or am I misunderstanding the CLT and its possible application to
simulations?

Undergrad: Stats
Grad: Comp Sci
Pro: Software Pathology

I think this question may be up my alley!

Taking sample means of simulations will make the distribution look
more like a normal distribution, but it won't necessarily make the
result being simulated any more accurate! That depends upon how
closely the simulation models reality. If the simulation is biased,
all that will happen by repeating the simulation is that you will get
a normal distribution with a mean of the biased mean.

For example: Let's say you were simulating the number of HCP that
North receives in a Bridge Hand, but you erroneously count the D7 as
being worth 10HCP. Sample means from your simulation, if otherwise
correct, would end up looking perfectly normal with a mean of 12.5. In
fact, the more sample means that you took and more simulations that
you ran, the closer the sample would look to a normal distribution
with a mean of 12.5. Your answer would never get anywhere close to the
proper value of 10.


.

Relevant Pages

  • Re: Question for the statisticians
    ... schrieb im Newsbeitrag ... "According to the first part of the Central Limit Theorem, ... variables tends toward a Gaussian distribution, ... not apply) to the issue of bridge simulations. ...
    (rec.games.bridge)
  • Re: 11 pts opposite weak NT
    ... run on a dealer using normal weak NT constraints (ie 4432,4333,5332 shapes ... Your have done enough simulations that the difference between your two ... On second thought I doubt that it matters, to the HC distribution, ... extrapolate that the missing lower right block -- the most relevant ...
    (rec.games.bridge)
  • Re: Question for the statisticians
    ... sampling distribution of means is a normal distribution if the ... not apply) to the issue of bridge simulations. ... answer is that you do not apply the Central Limit Theorem in any ...
    (rec.games.bridge)
  • Re: Question for the statisticians
    ... "According to the first part of the Central Limit Theorem, ... sampling distribution of means is a normal distribution if the ... If one were to run 30 separate 50 hand simulations of the same ...
    (rec.games.bridge)
  • Re: FFT test with few kbits
    ... say it routinely passes good random streams. ... empirical distribution of a statistic. ... determine the number of simulations that you need. ... because we must also show that a good RNG would not have failed as ...
    (sci.crypt)