Demo of central limit theorem

... import sys from pylab import * from pacal import *
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Using compiled interpolation routine

... colors = "kbgrcmy" def central_limit_demo(X, N = 5, xmin = None, xmax = None, ymax = None, args): figure() title("Limit of averages of " + X.getName()) X.plot(linewidth = 4, color = "c", args) Y = X print "Limit of averages of " + X.getName() + ": ", for i in xrange(N-1): print i+2, sys.stdout.flush() Y += X (Y/(i+2)).plot(color = colors[i%len(colors)], **args) if xmin is not None: xlim(xmin = xmin) if xmax is not None: xlim(xmax = xmax) ylim(ymin = 0) if ymax is not None: ylim(ymax = ymax) print show()
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uniform distribution

... X = UniformDistr(0,1) central_limit_demo(X, xmin=-0.1, xmax=1.1)
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Limit of averages of U(0,1):  2 3 4 5

... X = ChiSquareDistr(1) central_limit_demo(X, N=10, ymax=1.5, xmax=3)
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Limit of averages of Chi2(1):  2 3 4 5 6 7 8 9 10

... X = UniformDistr(1,3) / UniformDistr(-2,1) central_limit_demo(X, N = 5, xmin=-5, xmax=5)
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Limit of averages of U(1,3)/U(-2,1):  2 3 4 5

... X = CauchyDistr() central_limit_demo(X)
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Limit of averages of Cauchy(0.0,1.0):  2 3 4 5

... X = LevyDistr() central_limit_demo(X, xmax=10)
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Limit of averages of Levy(1.0,0.0):  2 3 4 5