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Registered Member #191
Joined: Fri Feb 17 2006, 02:01AM
Location: Esbjerg Denmark
Posts: 720
This is probably real simple, but im quite stuck here. Say I need a set of 100 numbers, normally distributed, with a mean of 10 and std of 0.3. How would i do that?
Registered Member #72
Joined: Thu Feb 09 2006, 08:29AM
Location: UK St. Albans
Posts: 1659
Several ways. You could try starting excel, then go Help - random, and follow the tortuous instructions about how to use the analysis tool (and to install the analysis tool if it isn't there) to generate numbers from a normal (or other) distribution.
Alternatively, it is fairly straightforward (I am told), to convert a pair of uniformly distributed randoms (which come from the RAND fujcntion) into a pair of normally distributed numbers. I came across this one day wwilfing. IIRC it was the Box-Muller transformation on the Wolfram MathWorld site.
There is another real brute-force way, that works quite well when efficieny is not an issue, and for 100 numbers it isn't. If you add together (say) 48 (statisticaly a lot) unifmrly 0-1 distributed rands, then the mean will be 24 (each is typically 0.5), and the std dev will be 2 (which is sqrt(48/12), I'll leave why that expression for the stddev as an excercise). The resulting distribution is not strictly normal, in that the minimum and maximum numbers are constrained to be 0 and 47.999, instead of +/- inifinity, but it's an adequate approximation for anything other than splitting hairs, how often do values outside +/- 12.sigma appear in a real normal distribution?
Registered Member #30
Joined: Fri Feb 03 2006, 10:52AM
Location: Glasgow, Scotland
Posts: 6706
This brute-force method is just the central limit theorem.
It works because that's how the normal distribution is defined to start with: the distribution you get when you add or average a bunch of random stuff together.
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Generating a Normally distributed set in excel, how?
