python 3.1 - Creating normal distribution

Question

I have scipy and numpy, Python v3.1

I need to create a 1D array of length 3million, using random numbers between (and including) 100-60,000. It has to fit a normal distribution.

Using 'a = numpy.random.standard_normal(3000000)', I get a normal distribution for that required length; not sure how to achieve the required range.

Answer 1

A standard normal distribution has mean 0 and standard deviation 1. What I understand from your requirements is that you need a ((60000-100)/2, (60000-100)/2) one. Take each value from standard_normal() result, multiply it by the new variance, and add the new mean.

I haven't used NumPy, but a quick search of the docs says that you can achieve what you want directly bu using numpy.random.normal()

One last tidbit: normal distributions are not bounded. That means there isn't a value with probability zero. Your requirements should be in terms of means and variances (or standard deviations), and not of limits.

Answer 2

If you want a truly random normal distribution, you can't guarentee how far the numbers will spread. You can reduce the probability of outliers, however, by specifying the standard deviation

>>> n = 3000000
>>> sigma5 = 1.0 / 1744278
>>> n * sigma5
1.7199093263803131  # Expect one values in 3 mil outside range at 5 stdev.
>>> sigma6 = 1.0 / 1 / 506800000
>>> sigma6 = 1.0 / 506800000
>>> n * sigma6
0.0059194948697711127 # Expect 0.005 values in 3 mil outside range at 6 stdev.
>>> sigma7 = 1.0 / 390600000000
>>> n * sigma7
7.6804915514592934e-06

Therefore, in this case, ensuring that the standard deviation is only 1/6 or 1/7 of half the range will give you reasonable confidence that your data will not exceed the range.

>>> range = 60000 - 100
>>> spread = (range / 2) / 6 # Anything outside of the range will be six std. dev. from the mean
>>> mean = (60000 + 100) / 2
>>> a = numpy.random.normal(loc = mean, scale = spread, size = n) 
>>> min(a)
6320.0238199673404
>>> max(a)
55044.015566089176

Of course, you can still can values that fall outside the range here