CHAPTER 5 - FUNCTIONS

... from functools import partial import numpy from pylab import figure, show from pacal import *
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Using compiled interpolation routine

... from pacal.distr import demo_distr
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Example 5.1.3

... d = NormalDistr() + NormalDistr() * NormalDistr() demo_distr(d)
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============= summary =============
  N(0.0,1.0)+N(0.0,1.0)*N(0.0,1.0)
                mean  =  2.22044604925e-16
                 std  =  1.41421356237
                 var  =  2.0
              median  =  0.0
            medianad  =  0.864135618196
      iqrange(0.025)  =  5.63838771975
               range  =  (-inf, inf)
            ci(0.05)  =  (-2.8191938598737281, 2.8191938598740514)
             int_err  =  -8.881784197e-16

...
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Example 5.5

... d = ExponentialDistr() / (ExponentialDistr() + ExponentialDistr()) figure() demo_distr(d, xmax=20, ymax=1.5)
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============= summary =============
  ExpD(1)/(ExpD(1)+ExpD(1))
                mean  =  1.0
                 std  =  inf
                 var  =  inf
              median  =  0.414213562373
            medianad  =  0.318580491791
      iqrange(0.025)  =  5.31181595325
               range  =  (0.0, inf)
            ci(0.05)  =  (0.012739367083666622, 5.3245553203367351)
             int_err  =  -2.22044604925e-16

...
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Exercise 5.5 part a

... figure() demo_distr(NormalDistr() / sqrt((NormalDistr()2 + NormalDistr()2) / 2), xmin=-3, xmax=3)
		.

============= summary =============
  N(0.0,1.0)/exp(0.5*log(0.5*(sqr(N(0.0,1.0))+sqr(N(0.0,1.0)))))
                mean  =  2.22044604925e-16
                 std  =  inf
                 var  =  inf
              median  =  0.0
            medianad  =  0.816496580928
      iqrange(0.025)  =  8.6053054595
               range  =  (-inf, inf)
            ci(0.05)  =  (-4.3026527297494699, 4.3026527297494095)
             int_err  =  -6.66133814775e-16

part b

... figure() demo_distr(2 * NormalDistr()2 / (NormalDistr()2 + NormalDistr()**2), xmax=20, ymax=2)
		.

============= summary =============
  (2*sqr(N(0.0,1.0)))/(sqr(N(0.0,1.0))+sqr(N(0.0,1.0)))
                mean  =  nan
                 std  =  nan
                 var  =  nan
              median  =  0.666666664933
            medianad  =  0.633525148605
      iqrange(0.025)  =  38.5050763413
               range  =  (0.0, inf)
            ci(0.05)  =  (0.0012507817364725586, 38.506327122991905)
             int_err  =  -1.26784627241e-09

part c

... figure() demo_distr(3 * NormalDistr()2 / (NormalDistr()2 + NormalDistr()2 + NormalDistr()2), xmax=20, ymax=2)
		.

============= summary =============
  (3*sqr(N(0.0,1.0)))/(sqr(N(0.0,1.0))+sqr(N(0.0,1.0))+sqr(N(0.0,1.0)))
                mean  =  3.00000290384
                 std  =  inf
                 var  =  inf
              median  =  0.585060274052
            medianad  =  0.550673034457
      iqrange(0.025)  =  17.4422851227
               range  =  (0.0, inf)
            ci(0.05)  =  (0.0011571891323882905, 17.44344231184073)
             int_err  =  -1.84488713195e-09

part d

... figure() demo_distr((NormalDistr()2 + NormalDistr()2) / (NormalDistr()2 + NormalDistr()2), xmax=20)
		.

============= summary =============
  (sqr(N(0.0,1.0))+sqr(N(0.0,1.0)))/(sqr(N(0.0,1.0))+sqr(N(0.0,1.0)))
                mean  =  nan
                 std  =  nan
                 var  =  nan
              median  =  1.0
            medianad  =  0.828427124746
      iqrange(0.025)  =  38.9743589744
               range  =  (0.0, inf)
            ci(0.05)  =  (0.025641025641025626, 38.999999999998309)
             int_err  =  -1.11022302463e-15

...
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Exercise 5.6

... d = sqrt(UniformDistr(0,1)2 + UniformDistr(0,1)2) # a bug in Springer?? def theor_ampl_uni(x): return (x<1)numpy.pi/2x + (x>=1)(2numpy.arcsin(1.0/x) - 0*numpy.pi/2) figure() #demo_distr(d, theoretical = theor_ampl_uni, histogram=True) demo_distr(d)
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============= summary =============
  exp(0.5*log(sqr(U(0,1))+sqr(U(0,1))))
                mean  =  0.765195581011
                 std  =  0.284854655401
                 var  =  0.0811421747037
              median  =  0.797884560803
            medianad  =  0.199471140201
      iqrange(0.025)  =  1.08115660638
               range  =  (0.0, 1.4142135623730949)
            ci(0.05)  =  (0.17841241161525598, 1.259569017999167)
             int_err  =  1.35453914085e-07

... show()
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