norm

numeric.stats.norm

A normal continuous random variable.

The probability density function for norm is:

\[f(x) = \frac{\exp(-x^2/2)}{\sqrt{2\pi}}\]

Examples:

from mipylib.numeric.stats import norm

x = arange(-5., 5., 0.01)
aa = [0, 0, 0, -2]
bb = [0.2, 1, 5, 0.5]
ss = ['-b', '-r', '-c', '-g']

#PDF
subplot(1,2,1)
for a,b,s in zip(aa,bb,ss):
    y = norm.pdf(x, a, sqrt(b))
    plot(x, y, s, linewidth=2, label=r'$\mu = %i, \sigma^2 = %.1f$' % (a, b))
legend(loc='upper left', facecolor='w')
ylim(0, 1)
xlim(-5.5, 5.5)
title('PDF')

#CDF
subplot(1,2,2)
for a,b,s in zip(aa,bb,ss):
    y = norm.cdf(x, a, sqrt(b))
    plot(x, y, s, linewidth=2, label=r'$\mu = %i, \sigma^2 = %.1f$' % (a, b))
legend(loc='lower right', facecolor='w')
ylim(0, 1)
xlim(-5.5, 5.5)
title('CDF')

suptitle('Normal distribution')