Distribution of Hill's tail exponent distribution

... from pacal import *
		.

Using compiled interpolation routine

... from pylab import figure, show def Hill_estim_distr(d, n, xmin): """The distribution of Hill's estimator for given distribution d >= xmin and sample size n.""" s = log(d / xmin) for i in xrange(n - 1): s += log(d / xmin) return 1 + n / s a = Hill_estim_distr(ParetoDistr(2, 1), 5, 1) a.summary()
		.

============= summary =============
  (5.0*((1/(log(Pareto(2,1))+log(Pareto(2,1))+log(Pareto(2,1))+log(Pareto(2,1))+log(Pareto(2,1))))))+1
                mean  =  3.5
                 std  =  1.44337567297
                 var  =  2.08333333333
              median  =  3.14091095565
            medianad  =  0.638370086855
      iqrange(0.025)  =  5.18317249607
               range  =  (1.0, inf)
            ci(0.05)  =  (1.9764110156084711, 7.1595835116738193)
             int_err  =  -1.11022302463e-15

... a.plot() show()
		.

... figure() a = Hill_estim_distr(ParetoDistr(1, 1), 10, 1) a.summary()
		.

============= summary =============
  (10.0*((1/(log(Pareto(1,1))+log(Pareto(1,1))+log(Pareto(1,1))+log(Pareto(1,1))+log(Pareto(1,1))+log(Pareto(1,1))+log(Pareto(1,1))+log(Pareto(1,1))+log(Pareto(1,1))+log(Pareto(1,1))))))+1
                mean  =  2.11111111111
                 std  =  0.392837100659
                 var  =  0.154320987654
              median  =  2.03426364294
            medianad  =  0.219358331595
      iqrange(0.025)  =  1.50002120798
               range  =  (1.0, inf)
            ci(0.05)  =  (1.585315483928994, 3.0853366919065133)
             int_err  =  -1.90958360236e-14

... a.plot() show()
		.