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Task/Verify-distribution-uniformity-Chi-squared-test/Python/verify-distribution-uniformity-chi-squared-test.py

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+import math
+import random
+
+def GammaInc_Q( a, x):
+    a1 = a-1
+    a2 = a-2
+    def f0( t ):
+        return t**a1*math.exp(-t)
+
+    def df0(t):
+        return (a1-t)*t**a2*math.exp(-t)
+
+    y = a1
+    while f0(y)*(x-y) >2.0e-8 and y < x: y += .3
+    if y > x: y = x
+
+    h = 3.0e-4
+    n = int(y/h)
+    h = y/n
+    hh = 0.5*h
+    gamax = h * sum( f0(t)+hh*df0(t) for t in ( h*j for j in xrange(n-1, -1, -1)))
+
+    return gamax/gamma_spounge(a)
+
+c = None
+def gamma_spounge( z):
+    global c
+    a = 12
+
+    if c is None:
+       k1_factrl = 1.0
+       c = []
+       c.append(math.sqrt(2.0*math.pi))
+       for k in range(1,a):
+          c.append( math.exp(a-k) * (a-k)**(k-0.5) / k1_factrl )
+          k1_factrl *= -k
+
+    accm = c[0]
+    for k in range(1,a):
+        accm += c[k] / (z+k)
+    accm *= math.exp( -(z+a)) * (z+a)**(z+0.5)
+    return accm/z;
+
+def chi2UniformDistance( dataSet ):
+    expected = sum(dataSet)*1.0/len(dataSet)
+    cntrd = (d-expected for d in dataSet)
+    return sum(x*x for x in cntrd)/expected
+
+def chi2Probability(dof, distance):
+    return 1.0 - GammaInc_Q( 0.5*dof, 0.5*distance)
+
+def chi2IsUniform(dataSet, significance):
+    dof = len(dataSet)-1
+    dist = chi2UniformDistance(dataSet)
+    return chi2Probability( dof, dist ) > significance
+
+dset1 = [ 199809, 200665, 199607, 200270, 199649 ]
+dset2 = [ 522573, 244456, 139979,  71531,  21461 ]
+
+for ds in (dset1, dset2):
+    print "Data set:", ds
+    dof = len(ds)-1
+    distance =chi2UniformDistance(ds)
+    print "dof: %d distance: %.4f" % (dof, distance),
+    prob = chi2Probability( dof, distance)
+    print "probability: %.4f"%prob,
+    print "uniform? ", "Yes"if chi2IsUniform(ds,0.05) else "No"