{
    "info": {
        "author": "Sergey Kim, Reidar Brumer Bratvold",
        "author_email": "kimsergeo@gmail.com, reidar.bratvold@uis.no",
        "bugtrack_url": null,
        "classifiers": [
            "Development Status :: 2 - Pre-Alpha",
            "License :: OSI Approved :: MIT License",
            "Programming Language :: Python",
            "Programming Language :: Python :: 3",
            "Programming Language :: Python :: 3.4",
            "Programming Language :: Python :: 3.5",
            "Programming Language :: Python :: 3.6",
            "Programming Language :: Python :: 3.7"
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        "description": "metalog\n=======\n\nSergey Kim, Reidar Brumer Bratvold\n\nMetalog Distribution\n--------------------\n\nThe metalog distributions constitute a new system of continuous\nunivariate probability distributions designed for flexibility,\nsimplicity, and ease/speed of use in practice. The system is comprised\nof unbounded, semi-bounded, and bounded distributions, each of which\noffers nearly unlimited shape flexibility compared to Pearson, Johnson,\nand other traditional systems of distributions.\n\nThe package requires the following packages: **numpy, pandas, matplotlib and scipy (ver 1.3.1)**.\n\nThe following\n`paper <http://www.metalogdistributions.com/images/TheMetalogDistributions.pdf>`__\nand `website <http://www.metalogdistributions.com/home.html>`__ provide\na full background of the metalog distribution.\n\nUsing the Package\n-----------------\n\nThis Python package was transfered from\n`RMetalog <https://github.com/isaacfab/RMetalog>`__ package by Isaac J.\nFaber and therefore shares the same R-based structure.\n\nThe\n`data <https://www.sciencebase.gov/catalog/item/5b45380fe4b060350a140b7b>`__\nused for demonstration are body length of salmon and were collected in\n2008-2010:\n\n::\n\n    import numpy as np\n    import pandas as pd\n\n    salmon = pd.read_csv(\"Chinook and forage fish lengths.csv\")\n\n    # Filtered data for eelgrass vegetation and chinook salmon\n    salmon = salmon[(salmon['Vegetation'] == 'Eelgrass') & (salmon['Species'] == 'Chinook_salmon')]\n    salmon = np.array(salmon['Length'])\n\nTo import package with metalog distribution run the code:\n\n::\n\n    from metalog import metalog\n\nTo **fit the data to metalog distribution** one should use function\n``metalog.fit()``. It has the following arguments:\n\n-  ``x``: data.\n\n-  ``bounds``: bounds of metalog distribution. Depending on\n   ``boundedness`` argument can take zero, one or two values.\n\n-  ``boundedness``: boundedness of metalog distribution. Can take values\n   ``'u'`` for unbounded, ``'sl'`` for semi-bounded lower, ``'su'`` for\n   semi-bounded upper and ``'b'`` for bounded on both sides.\n\n-  ``term_limit``: maximum number of terms to specify the metalog\n   distribution. Can take values from 3 to 30.\n\n-  ``term_lower_bound``: the lowest number of terms to specify the\n   metalog distribution. Must be greater or equal to 2 and less than\n   ``term_limit``. The argument is optional. Default value is 2.\n\n-  ``step_len``: size of steps to summarize the distribution. The\n   argument is optional. Default value is 0.01.\n\n-  ``probs``: probabilities corresponding to data. The argument is\n   optional. Default value is ``numpy.nan``.\n\n-  ``fit_method``: fit method ``'OLS'``, ``'LP'`` or ``'any'``. The\n   argument is optional. Default value is ``'any'``.\n\n-  ``save_data``: if ``True`` then data will be saved for future update.\n   The argument is optional. Default values is ``False``.\n\nFit metalog distribution to data and store the result to variable\n``metalog_salmon``. The distribution is bounded on both sides: from 0 to\n200. Term limit is set to 10:\n\n::\n\n    metalog_salmon = metalog.fit(x=salmon, boundedness='b', bounds=[0, 200], term_limit=10)\n\nTo get **summary of distribution** call the following function with only\none argument ``m`` - the variable that stores fitted metalog\ndistribution:\n\n::\n\n    metalog.summary(m=metalog_salmon)\n\nOutput:\n\n::\n\n     -----------------------------------------------\n     SUMMARY OF METALOG DISTRIBUTION OBJECT\n     -----------------------------------------------\n\n    PARAMETERS\n\n     Term Limit:  10 \n     Term Lower Bound:  2 \n     Boundedness:  b \n     Bounds (only used based on boundedness):  [0, 200] \n     Step Length for Distribution Summary:  0.01 \n     Method Use for Fitting:  any \n     Number of Data Points Used:  138 \n     Original Data Saved:  False \n\n\n    VALIDATION AND FIT METHOD\n\n         term valid method\n    2      2   yes    OLS\n    3      3   yes    OLS\n    4      4   yes    OLS\n    5      5   yes    OLS\n    6      6   yes    OLS\n    7      7   yes    OLS\n    8      8   yes    OLS\n    9      9   yes    OLS\n    10    10   yes    OLS\n\nIt's possible **to plot corresponding PDF and CDF** of metalog\ndistribution:\n\n::\n\n    metalog.plot(m=metalog_salmon)\n\nOutput:\n\n.. figure:: https://raw.githubusercontent.com/kimsergeo/metalog/master/figures/figure_1.png\n   :alt: pdf\\_cdf\n\n**To draw samples** from distribution use ``metalog.r()`` function where\n``n`` is number of samples and ``term`` specifies the terms of\ndistribution to sample from:\n\n::\n\n    metalog.r(m=metalog_salmon, n=5, term=10)\n\nOutput:\n\n::\n\n    array([73.81897286, 86.74055734, 84.22509619, 83.80426247, 97.79800677])\n\n**To get densities** based on quantiles type ``metalog.d()`` function\nwhere ``q`` is vector of quantiles:\n\n::\n\n    metalog.d(m=metalog_salmon, q=[50, 110, 150], term=10)\n\nOutput:\n\n::\n\n    array([0.00038265, 0.00712032, 0.00373991])\n\n**To calculate probabilities** based on quantiles use ``metalog.p()``\nfunction:\n\n::\n\n    metalog.p(m=metalog_salmon, q=[50, 110, 150], term=10)\n\nOutput:\n\n::\n\n    array([0.00275336, 0.82349578, 0.98686581])\n\nFinally, **to get quantiles** from probabilites input ``metalog.q()``:\n\n::\n\n    metalog.q(m=metalog_salmon, y=[0.00275336, 0.82349578, 0.98686581], term=10)\n\nOutput:\n\n::\n\n    array([ 50.02583336, 109.99861143, 149.99737059])\n\n\n\n",
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