Random.nextGaussian() is supposed to give random no.s with mean 0 and std deviation 1. Many no.s it generated are outside range of [-1,+1]. how can i set so that it gives normally distributed random no.s only in the range -1 to 1.
+5
A:
A normal distribution gives a non-zero (but "becoming extremely small") probability of seeing values outside [-1, +1] whatever variance you give - you're just squishing the curve, effectively.
You could use a small variance and then just run the results through a map which cropped anything less than -1 to -1, and anything greater than 1 to 1, but it wouldn't (strictly speaking) be a normal distribution any more.
What do you need this distribution for, out of interest?
Jon Skeet
2009-03-10 11:53:04
It's not that small. Close to 30% of the values have to be outside 1 standard deviation. Something like 5% will lie outside 2 standard deviations.
S.Lott
2009-03-10 11:58:41
The "becoming extremely small" was intended to imply that as you get further away from the mean, the probability of generating the value gets smaller, but still non-zero.
Jon Skeet
2009-03-10 12:01:32
i am implementing a statistical analysis program. It uses normal distibution.
BHARATH
2009-03-10 12:11:34
BHARATH, If your statistical program requires a normal distribution, why do you not want to use a normal distribution, i.e. why don't you want to let it have its natural range?
John D. Cook
2009-03-10 12:20:27
+1 to John's comment.
Jon Skeet
2009-03-10 12:31:54
+8
A:
Doesn't the normal distribution include numbers arbitrarily far from the mean, but with increasingly small probabilities? It might be that your desires (normal and limited to a specific range) are incompatible.
Ned Batchelder
2009-03-10 11:54:12
+7
A:
A Gaussian distribution with a mean 0 and standard deviation one means that the average of the distribution is 0 and about 70% of the population lies in the range [-1, 1]. Ignore the numbers that are outside your range -- they form the fringe 16% approx on either side.
Maybe a better solution is to generate a distribution with mean=0 and std.dev=0.5. This will give you a distribution with about 96% of the values in the range [-1, 1].
An even better solution is to work backward as above and use the idea that approx. 99.7% of the values lie in the 3-sigma range: use a std.dev = 1/3. That will almost nullify the amount of not-so-useful values that you are getting. When you do get one, omit it.
Of course, if you are working on a math intensive product, all of this bears no value.
dirkgently
2009-03-10 11:55:16
Except, of course, ignoring those numbers means that your random values aren't really normal any more, are they?
S.Lott
2009-03-10 11:57:12
By that definition, any clamping you do on any random number generator is introducing a bias.
dirkgently
2009-03-10 12:03:56
@dirkgently: Absolutely. It's not a normal distribution any more, just one which is "quite like" a normal distribution.
Jon Skeet
2009-03-10 12:32:28
@Jon Skeet: I understand the implications of my suggestion. I'm only saying that S. Lott's observations are right on spot and the OP's question is a paradoxical one. Mais,c'est la vie.
dirkgently
2009-03-10 12:43:35
+1
A:
A standard deviation of 1.0 entails that many values will lie outside the [-1,1] range.
If you need to keep within this range, you should use another method, perhaps nextDouble().
Tor Haugen
2009-03-10 11:56:15
+1
A:
Gaussian distribution with your parameters. is has density e^(-x^2/2). In general it is of the form e^(linear(x)+linear(x^2)) which means whatever settings you give it, you have some probability of getting very large and very small numbers.
You are probably looking for some other distribution.
SurDin
2009-03-10 12:05:04