Re: random generation
- From: "nitish" <nitishkum@xxxxxxxxx>
- Date: 6 Jul 2006 01:56:34 -0700
thanks for ur mail. its very informative.now my next question will be
that how can i generate random numbers for some distribution in any
statistical package like SPSS or Statistica. I am working as a tec
consultant for Statistica software in a company called Statsoft india.
I am aware of random number generation theory since i have done masters
in statistics. only thing is that i am not able to do it in Statistica
software.
Old Mac User wrote:
There are so many uses for random numbers that I cannot begin to
discuss all of them.
Cryptography is one. Simulations of complex systems is another. I use
them frequently to create training materials... demonstrations that I
can use to teach principles of statistics and related subjects. If you
know just a little about statistics and want to learn a lot about it in
a hurry, simulations are fast and convincing. True, we like to have
closed form expressions for everything. But we can't have that, and
those expressions are often so complex that we cannot grasp the essence
of the matter.
In order to generate random numbers from different statistical
distributions, we need a random number generator. This usually means
generating uniform random numbers on the scale of 0 to 1. There are
specific "recipes" for converting those uniform random numbers into a
normal distribution. Or a Poisson distribution. Or to whatever
distribution we want that that moment. If you want some of those
"recipes" I can send them to you.
Send an e-mail to hedging77 followed by the usual symbol for "at" and
then google.com
There have been many heated discussions about the "quality" of random
number generators. There are several useful tests for randomness.
There are also certain subtle issue about hidden patterns in the
pseudo-random numbers generated with software on computers. Those
subtle patterns can become a "big deal" in certain circumstance, but
there are ways to overcome them easily.
So what's random and what's pseudo-random? In one sense "random" means
numbers that vary totally out of our control... like emissions from a
radioactive source. Pseudo-random implies an algorithm on a computer.
If we get the same sequence of numbers every time we run the algorithm
then those are called pseudo-random numbers. This is not necessarily a
bad thing. When writing and debugging software that involves generating
and working wirh random numbers, it's good to be able to run the same
numbers again-and-again as we change the code. But then there comes a
point at which we want to make production runs and we want sequences of
numbers that are "out of our control." This is usually done by making
a small change in the instructions to the random number generator to
tell it to start the sequence from the clock on the computer.
One way to think about "random" is this. If I tell you the first N
numbers in a sequence of random numbers then you cannot tell me what
the N + 1 th number will be.
That brings us to one more point. Most random number generators on a
computer will eventually repeat their cycles. So if the first two
random numbers are 0.34167 and 0.02345 then at some point in the
future... maybe 400,000,000 random numbers later... we'll get 0.34167
and 0.02345 etc. again. This, of course, will be a pseudo-random number
sequence. Starting it from the computer clock doesn't get rid of the
cycles. The cycle length is important. If you try to write your own
random number generator it may have a very short cycle length. There
are rules for making the cycle length as large as possible.
There are simple ways to avoid getting entangled in issues about hidden
patterns and cycle lengths and other things that could make
pseudo-random numbers become troublesome in large and long simulations.
If you are just using a random number gnerator to learn something about
variation and statistics, don't get lost in the fine details of these
things. For most work "pseudo-random" is good enough.
On the other hand, people who do serious work in cryptology do need to
be very concerned about these matters. Reason: Since pseudo-random
numbers arrive in specific sequences, if you learn a little about that
sequence then you can reproduce all of it. That's one way to break a
code. This is why you see some intense discussions about "random" vs.
"pseudo-random". OMU
nitish wrote:
my question to you all is that why do we generate random numbers for
diffrent distributions( say normal). what is the meaning of pseudo
random numbers.
.
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