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"description": "RunStats: Computing Statistics and Regression in One Pass\n=========================================================\n\n`RunStats`_ is an Apache2 licensed Python module for online statistics and\nonline regression. Statistics and regression summaries are computed in a single\npass. Previous values are not recorded in summaries.\n\nLong running systems often generate numbers summarizing performance. It could\nbe the latency of a response or the time between requests. It's often useful to\nuse these numbers in summary statistics like the arithmetic mean, minimum,\nstandard deviation, etc. When many values are generated, computing these\nsummaries can be computationally intensive. It may even be infeasible to keep\nevery recorded value. In such cases computing online statistics and online\nregression is necessary.\n\nIn other cases, you may only have one opportunity to observe all the recorded\nvalues. Python's generators work exactly this way. Traditional methods for\ncalculating the variance and other higher moments requires multiple passes over\nthe data. With generators, this is not possible and so computing statistics in\na single pass is necessary.\n\nThe Python `RunStats`_ module was designed for these cases by providing a pair\nof classes for computing online summary statistics and online linear regression\nin a single pass. Summary objects work on sequences which may be larger than\nmemory or disk space permit. They may also be efficiently combined together to\ncreate aggregate summaries.\n\nFeatures\n--------\n\n- Pure-Python\n- Fully Documented\n- 100% Test Coverage\n- Numerically Stable\n- Optional Cython-optimized Extension (20-40 times faster)\n- Statistics summary computes mean, variance, standard deviation, skewness,\n kurtosis, minimum and maximum.\n- Regression summary computes slope, intercept and correlation.\n- Developed on Python 3.7\n- Tested on CPython 2.7, 3.4, 3.5, 3.6, 3.7 and PyPy, PyPy3\n- Tested using Travis CI\n\n.. image:: https://api.travis-ci.org/grantjenks/python-runstats.svg?branch=master\n :target: http://www.grantjenks.com/docs/runstats/\n\n.. image:: https://ci.appveyor.com/api/projects/status/github/grantjenks/python-runstats?branch=master&svg=true\n :target: http://www.grantjenks.com/docs/runstats/\n\nQuickstart\n----------\n\nInstalling `RunStats`_ is simple with `pip `_::\n\n $ pip install runstats\n\nIf you want the Cython-optimized version then first install `Cython\n`_::\n\n $ pip install cython\n $ pip install runstats\n\nYou can access documentation in the interpreter with Python's built-in help\nfunction:\n\n.. code-block:: python\n\n >>> from runstats import Statistics, Regression\n >>> help(Statistics)\n >>> help(Regression)\n\nTutorial\n--------\n\nThe Python `RunStats`_ module provides two types for computing running\nStatistics and Regression. The Regression object leverages Statistics\ninternally for its calculations. Each can be initialized without arguments:\n\n.. code-block:: python\n\n >>> from runstats import Statistics, Regression\n >>> stats = Statistics()\n >>> regr = Regression()\n\nStatistics objects support four methods for modification. Use `push` to add\nvalues to the summary, `clear` to reset the summary, sum to combine Statistics\nsummaries and multiply to weight summary Statistics by a scalar.\n\n.. code-block:: python\n\n >>> for num in range(10):\n ... stats.push(num)\n >>> stats.mean()\n 4.5\n >>> stats.maximum()\n 9\n >>> stats += stats\n >>> stats.mean()\n 4.5\n >>> stats.variance()\n 8.68421052631579\n >>> len(stats)\n 20\n >>> stats *= 2\n >>> len(stats)\n 40\n >>> stats.clear()\n >>> len(stats)\n 0\n >>> stats.minimum() is None\n True\n\nUse the Python built-in `len` for the number of pushed values. Unfortunately\nthe Python `min` and `max` built-ins may not be used for the minimum and\nmaximum as sequences are instead expected. There are instead `minimum` and\n`maximum` methods which are provided for that purpose:\n\n.. code-block:: python\n\n >>> import random\n >>> random.seed(0)\n >>> for __ in range(1000):\n ... stats.push(random.random())\n >>> len(stats)\n 1000\n >>> min(stats)\n Traceback (most recent call last):\n ...\n TypeError: iteration over non-sequence\n >>> stats.minimum()\n 0.00024069652516689466\n >>> stats.maximum()\n 0.9996851255769114\n\nStatistics summaries provide five measures of a series: mean, variance,\nstandard deviation, skewness and kurtosis:\n\n.. code-block:: python\n\n >>> stats = Statistics([1, 2, 5, 12, 5, 2, 1])\n >>> stats.mean()\n 4.0\n >>> stats.variance()\n 15.33333333333333\n >>> stats.stddev()\n 3.915780041490243\n >>> stats.skewness()\n 1.33122127314735\n >>> stats.kurtosis()\n 0.5496219281663506\n\nAll internal calculations use Python's `float` type.\n\nLike Statistics, the Regression type supports some methods for modification:\n`push`, `clear` and sum:\n\n.. code-block:: python\n\n >>> regr.clear()\n >>> len(regr)\n 0\n >>> for num in range(10):\n ... regr.push(num, num + 5)\n >>> len(regr)\n 10\n >>> regr.slope()\n 1.0\n >>> more = Regression((num, num + 5) for num in range(10, 20))\n >>> total = regr + more\n >>> len(total)\n 20\n >>> total.slope()\n 1.0\n >>> total.intercept()\n 5.0\n >>> total.correlation()\n 1.0\n\nRegression summaries provide three measures of a series of pairs: slope,\nintercept and correlation. Note that, as a regression, the points need not\nexactly lie on a line:\n\n.. code-block:: python\n\n >>> regr = Regression([(1.2, 1.9), (3, 5.1), (4.9, 8.1), (7, 11)])\n >>> regr.slope()\n 1.5668320150154176\n >>> regr.intercept()\n 0.21850113956294415\n >>> regr.correlation()\n 0.9983810791694997\n\nBoth constructors accept an optional iterable that is consumed and pushed into\nthe summary. Note that you may pass a generator as an iterable and the\ngenerator will be entirely consumed.\n\nAll internal calculations are based entirely on the C++ code by John Cook as\nposted in a couple of articles:\n\n* `Computing Skewness and Kurtosis in One Pass`_\n* `Computing Linear Regression in One Pass`_\n\n.. _`Computing Skewness and Kurtosis in One Pass`: http://www.johndcook.com/blog/skewness_kurtosis/\n.. _`Computing Linear Regression in One Pass`: http://www.johndcook.com/blog/running_regression/\n\nThe pure-Python and Cython-optimized versions of `RunStats`_ are each directly\navailable if preferred.\n\n.. code-block:: python\n\n >>> from runstats.core import Statistics, Regression # pure-Python\n >>> from runstats.fast import Statistics, Regression # Cython-optimized\n\nWhen importing from `runstats` the `fast` version is preferred and the `core`\nversion is used as fallback. Micro-benchmarking Statistics and Regression by\ncalling `push` repeatedly shows the Cython-optimized extension as 20-40 times\nfaster than the pure-Python extension.\n\n.. _`RunStats`: http://www.grantjenks.com/docs/runstats/\n\nReference and Indices\n---------------------\n\n* `RunStats Documentation`_\n* `RunStats API Reference`_\n* `RunStats at PyPI`_\n* `RunStats at GitHub`_\n* `RunStats Issue Tracker`_\n\n.. _`RunStats Documentation`: http://www.grantjenks.com/docs/runstats/\n.. _`RunStats API Reference`: http://www.grantjenks.com/docs/runstats/api.html\n.. _`RunStats at PyPI`: https://pypi.python.org/pypi/runstats/\n.. _`RunStats at GitHub`: https://github.com/grantjenks/python-runstats/\n.. _`RunStats Issue Tracker`: https://github.com/grantjenks/python-runstats/issues/\n\nLicense\n-------\n\nCopyright 2013-2019 Grant Jenks\n\nLicensed under the Apache License, Version 2.0 (the \"License\"); you may not use\nthis file except in compliance with the License. You may obtain a copy of the\nLicense at\n\n http://www.apache.org/licenses/LICENSE-2.0\n\nUnless required by applicable law or agreed to in writing, software distributed\nunder the License is distributed on an \"AS IS\" BASIS, WITHOUT WARRANTIES OR\nCONDITIONS OF ANY KIND, either express or implied. See the License for the\nspecific language governing permissions and limitations under the License.",
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