For various ranges of "parameters", I routinely generate the same quantity of
random numbers using the Data Analysis, Random Number Generation function
("uniform" distribution).

Because I need to be be able to reproduce the random numbers, I choose a
"Random Seed" number.

My observations/questions are as follows:

Are the random numbers returned for a certain seed number indeed random
according to a uniform distribution? Are the "seed-related" random numbers
any less random than random numbers returned without using a seed number? I
ask because there appears to be a linear pattern with the first random number
returned for seeds 1, 2, 3, 4, etc., for a specified range of parameters.

Is there a range of seed numbers that one must stay within when choosing
random numbers from a specific range of parameters. For example, for
parameters 1 to 1,000, must one choose a seed number from 1 to 1,000?

In general, are there any guidelines/limitations inherent with Excel that I
should keep in mind when assigning a seed number? Also, is there a
"standard" random number generator that practicing scientists and engineers
typically use other than Excel?

Thanks for any assistance you can provide.......

Summary:
- Excel's "uniform" distribution function generates random numbers according to a uniform distribution with a specified seed number.
- The first random number generated by the algorithm follows a predictable pattern based solely on the seed number, but subsequent random numbers are truly random and uniform.
- There is no specific range of seed numbers to stay within, but it's generally a good idea to choose a seed number that is easy to remember or document.
- Excel's random number generator is a pseudo-random number generator, which can lead to patterns or biases in the generated numbers.
- To mitigate this issue, you can use a different random number generator, such as the Mersenne Twister algorithm, or third-party add-ins for Excel.

Steps to mitigate issues with Excel's random number generator:

1. Consider using a different random number generator, such as the Mersenne Twister algorithm.
2. Use third-party add-ins for Excel that provide more advanced random number generation capabilities.
3. Use a larger sample size or a larger range of parameters to reduce the likelihood of patterns or biases in the generated numbers.

Random number generators produce pseudo random numbers. The numbers are not
random as you have shown in that they are reproducible. Most random number
generators use an algorithm that produces numbers between 0 and 1 inclusive
from a uniform distribution. The generator produces a set sequence of
numbers - so think of it as a fixed list of numbers. the list is finite.
You might think of it as a circular list. then the seed determines where
you enter the list in the circle (this is a calculation however; seed 2 does
not start in the next number after seed 1). If the period of the list
(number of entries) is too small, then you could get repeating numbers - you
would start through the circle again.

I would assume the Excel random number generator has passed statistical
tests to show that it does a credible job of generating random numbers. I
have seen it criticized here as not being particularly good (although
concern would probably depend on what you are doing). I believe it was
improved in excel 2003.

As far as a standard, I don't believe such exists - I am sure there are many
opinions on what is the best way. You should be able to find algorithms for
generating random numbers on the web or in books such as numerical recipies
in C.

here is an article on the rand function in xl2003:
http://support.microsoft.com/default...b;en-us;828795
It also talks about the Rand function in earlier versions.

This article tells us that the Analysis toolpak uses its own random number
generator and this was not improved in xl2003. It is similar to that used
in earlier versions of Excel:
http://support.microsoft.com/default...b;en-us;829208


Here is an article on the VBA rnd function:
http://support.microsoft.com/default...b;en-us;231847

--
Regards,
Tom Ogilvy


"darebo" wrote in message
...
For various ranges of "parameters", I routinely generate the same quantity
of
random numbers using the Data Analysis, Random Number Generation function
("uniform" distribution).

Because I need to be be able to reproduce the random numbers, I choose a
"Random Seed" number.

My observations/questions are as follows:

Are the random numbers returned for a certain seed number indeed random
according to a uniform distribution? Are the "seed-related" random
numbers
any less random than random numbers returned without using a seed number?
I
ask because there appears to be a linear pattern with the first random
number
returned for seeds 1, 2, 3, 4, etc., for a specified range of parameters.

Is there a range of seed numbers that one must stay within when choosing
random numbers from a specific range of parameters. For example, for
parameters 1 to 1,000, must one choose a seed number from 1 to 1,000?

In general, are there any guidelines/limitations inherent with Excel that
I
should keep in mind when assigning a seed number? Also, is there a
"standard" random number generator that practicing scientists and
engineers
typically use other than Excel?

Thanks for any assistance you can provide.......

Thank you for your reply and references to other articles.....will you please
comment on the question I included in my original posting:

Is there a range of seed numbers that one must stay within when choosing
random numbers from a specific range of parameters. For example, for
parameters 1 to 1,000, must one choose a seed number from 1 to 1,000?

"Tom Ogilvy" wrote:

Random number generators produce pseudo random numbers. The numbers are not
random as you have shown in that they are reproducible. Most random number
generators use an algorithm that produces numbers between 0 and 1 inclusive
from a uniform distribution. The generator produces a set sequence of
numbers - so think of it as a fixed list of numbers. the list is finite.
You might think of it as a circular list. then the seed determines where
you enter the list in the circle (this is a calculation however; seed 2 does
not start in the next number after seed 1). If the period of the list
(number of entries) is too small, then you could get repeating numbers - you
would start through the circle again.

I would assume the Excel random number generator has passed statistical
tests to show that it does a credible job of generating random numbers. I
have seen it criticized here as not being particularly good (although
concern would probably depend on what you are doing). I believe it was
improved in excel 2003.

As far as a standard, I don't believe such exists - I am sure there are many
opinions on what is the best way. You should be able to find algorithms for
generating random numbers on the web or in books such as numerical recipies
in C.

here is an article on the rand function in xl2003:
http://support.microsoft.com/default...b;en-us;828795
It also talks about the Rand function in earlier versions.

This article tells us that the Analysis toolpak uses its own random number
generator and this was not improved in xl2003. It is similar to that used
in earlier versions of Excel:
http://support.microsoft.com/default...b;en-us;829208


Here is an article on the VBA rnd function:
http://support.microsoft.com/default...b;en-us;231847

--
Regards,
Tom Ogilvy


"darebo" wrote in message
...
For various ranges of "parameters", I routinely generate the same quantity
of
random numbers using the Data Analysis, Random Number Generation function
("uniform" distribution).

Because I need to be be able to reproduce the random numbers, I choose a
"Random Seed" number.

My observations/questions are as follows:

Are the random numbers returned for a certain seed number indeed random
according to a uniform distribution? Are the "seed-related" random
numbers
any less random than random numbers returned without using a seed number?
I
ask because there appears to be a linear pattern with the first random
number
returned for seeds 1, 2, 3, 4, etc., for a specified range of parameters.

Is there a range of seed numbers that one must stay within when choosing
random numbers from a specific range of parameters. For example, for
parameters 1 to 1,000, must one choose a seed number from 1 to 1,000?

In general, are there any guidelines/limitations inherent with Excel that
I
should keep in mind when assigning a seed number? Also, is there a
"standard" random number generator that practicing scientists and
engineers
typically use other than Excel?

Thanks for any assistance you can provide.......