powerlaw.ipynb

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      "Requirement already satisfied: powerlaw in /Users/peter/opt/anaconda3/lib/python3.7/site-packages (1.4.6)\r\n",
      "Requirement already satisfied: numpy in /Users/peter/opt/anaconda3/lib/python3.7/site-packages (from powerlaw) (1.18.1)\r\n",
      "Requirement already satisfied: mpmath in /Users/peter/opt/anaconda3/lib/python3.7/site-packages (from powerlaw) (1.1.0)\r\n",
      "Requirement already satisfied: matplotlib in /Users/peter/opt/anaconda3/lib/python3.7/site-packages (from powerlaw) (3.1.3)\r\n",
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   "source": [
    "# documentation\n",
    "# -- https://github.com/jeffalstott/powerlaw\n",
    "# -- https://arxiv.org/pdf/1305.0215.pdf\n",
    "\n",
    "!pip install powerlaw"
   ]
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   "source": [
    "# load the data \n",
    "data = [1, 1, 1, 2, 2, 3, 3, 4, 4, 4, 8, 8, 16]\n",
    "# NB: these are the (ordered) sizes of all SCCs, not the frequencies per bin"
   ]
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     "text": [
      "alpha  2.342900692497361\n",
      "xmin   3.0\n",
      "D      0.14223515510867168\n"
     ]
    },
    {
     "name": "stderr",
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     "text": [
      "Calculating best minimal value for power law fit\n"
     ]
    }
   ],
   "source": [
    "import powerlaw\n",
    "\n",
    "results = powerlaw.Fit(data, discrete=True) # if data has less than \n",
    "\n",
    "print('alpha ', results.power_law.alpha) # exponent of the best fitting powerlaw distribution\n",
    "print('xmin  ', results.power_law.xmin)  # value from which the powerlaw takes effect\n",
    "print('D     ', results.power_law.D)     # goodness-of-fit: KS distance between the fitted law \n",
    "                                         # and the emprical distribution. The smaller, the more likely the powerlaw\n",
    "                                         # assumption is to be correct."
   ]
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     "text": [
      "likelihood ratio -0.3257441865401183\n",
      "p value 0.5224495836658524\n"
     ]
    }
   ],
   "source": [
    "# Likelihood ratio test with an alternative assumption for the distribution family (log normal, exponential, etc).\n",
    "# -- we don't need this for the gamma/delta metrics, but it might be nice to run for the plot in 5.4\n",
    "\n",
    "R, p = results.distribution_compare('power_law', 'lognormal')\n",
    "\n",
    "print('likelihood ratio', R)\n",
    "# far from zero means it's likely one or the other. Positive means it's a power law, negative lognormal.\n",
    "print('p value', p)\n",
    "# p value for the conclusion."
   ]
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