Generating normal distribution in order python, numpy

Question

I am able to generate random samples of normal distribution in numpy like this.

>>> mu, sigma = 0, 0.1 # mean and standard deviation
>>> s = np.random.normal(mu, sigma, 1000)

But they are in random order, obviously. How can I generate numbers in order, that is, values should rise and fall like in a normal distribution.

In other words, I want to create a curve (gaussian) with mu and sigma and n number of points which I can input.

How to do this?

Answer 1

To (1) generate a random sample of x-coordinates of size n (from the normal distribution) (2) evaluate the normal distribution at the x-values (3) sort the x-values by the magnitude of the normal distribution at their positions, this will do the trick:

import numpy as np

mu,sigma,n = 0.,1.,1000

def normal(x,mu,sigma):
    return ( 2.*np.pi*sigma**2. )**-.5 * np.exp( -.5 * (x-mu)**2. / sigma**2. )

x = np.random.normal(mu,sigma,n) #generate random list of points from normal distribution
y = normal(x,mu,sigma) #evaluate the probability density at each point
x,y = x[np.argsort(y)],np.sort(y) #sort according to the probability density