stochastic
==========
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A python package for generating realizations of stochastic processes.
Installation
------------
The ``stochastic`` package is available on pypi and can be installed using pip
.. code-block:: shell
pip install stochastic
Dependencies
~~~~~~~~~~~~
Stochastic uses ``numpy`` for many calculations and ``scipy`` for sampling
specific random variables.
Processes
---------
This package offers a number of common discrete-time, continuous-time, and
noise process objects for generating realizations of stochastic processes as
``numpy`` arrays.
The diffusion processes are approximated using the Euler–Maruyama method.
Here are the currently supported processes and their class references within
the package.
* stochastic.processes
* continuous
* BesselProcess
* BrownianBridge
* BrownianExcursion
* BrownianMeander
* BrownianMotion
* CauchyProcess
* FractionalBrownianMotion
* GammaProcess
* GeometricBrownianMotion
* InverseGaussianProcess
* MixedPoissonProcess
* MultifractionalBrownianMotion
* PoissonProcess
* SquaredBesselProcess
* VarianceGammaProcess
* WienerProcess
* diffusion
* DiffusionProcess (generalized)
* ConstantElasticityVarianceProcess
* CoxIngersollRossProcess
* ExtendedVasicekProcess
* OrnsteinUhlenbeckProcess
* VasicekProcess
* discrete
* BernoulliProcess
* ChineseRestaurantProcess
* DirichletProcess
* MarkovChain
* MoranProcess
* RandomWalk
* noise
* BlueNoise
* BrownianNoise
* ColoredNoise
* PinkNoise
* RedNoise
* VioletNoise
* WhiteNoise
* FractionalGaussianNoise
* GaussianNoise
Usage patterns
--------------
Sampling
~~~~~~~~
To use ``stochastic``, import the process you want and instantiate with the
required parameters. Every process class has a ``sample`` method for generating
realizations. The ``sample`` methods accept a parameter ``n`` for the quantity
of steps in the realization, but others (Poisson, for instance) may take
additional parameters. Parameters can be accessed as attributes of the
instance.
.. code-block:: python
from stochastic.processes.discrete import BernoulliProcess
bp = BernoulliProcess(p=0.6)
s = bp.sample(16)
success_probability = bp.p
Continuous processes provide a default parameter, ``t``, which indicates the
maximum time of the process realizations. The default value is 1. The sample
method will generate ``n`` equally spaced increments on the
interval ``[0, t]``.
Sampling at specific times
~~~~~~~~~~~~~~~~~~~~~~~~~~
Some continuous processes also provide a ``sample_at()`` method, in which a
sequence of time values can be passed at which the object will generate a
realization. This method ignores the parameter, ``t``, specified on
instantiation.
.. code-block:: python
from stochastic.processes.continuous import BrownianMotion
bm = BrownianMotion(drift=1, scale=1, t=1)
times = [0, 3, 10, 11, 11.2, 20]
s = bm.sample_at(times)
Sample times
~~~~~~~~~~~~
Continuous processes also provide a method ``times()`` which generates the time
values (using ``numpy.linspace``) corresponding to a realization of ``n``
steps. This is particularly useful for plotting your samples.
.. code-block:: python
import matplotlib.pyplot as plt
from stochastic.processes.continuous import FractionalBrownianMotion
fbm = FractionalBrownianMotion(hurst=0.7, t=1)
s = fbm.sample(32)
times = fbm.times(32)
plt.plot(times, s)
plt.show()
Specifying an algorithm
~~~~~~~~~~~~~~~~~~~~~~~
Some processes provide an optional parameter ``algorithm``, in which one can
specify which algorithm to use to generate the realization using the
``sample()`` or ``sample_at()`` methods. See the documentation for
process-specific implementations.
.. code-block:: python
from stochastic.processes.noise import FractionalGaussianNoise
fgn = FractionalGaussianNoise(hurst=0.6, t=1)
s = fgn.sample(32, algorithm='hosking')
Raw data
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"description": "stochastic\n==========\n\n|build| |rtd| |codecov| |pypi| |pyversions|\n\n.. |build| image:: https://github.com/crflynn/stochastic/actions/workflows/build.yml/badge.svg\n :target: https://github.com/crflynn/stochastic/actions\n\n.. |rtd| image:: https://img.shields.io/readthedocs/stochastic.svg\n :target: http://stochastic.readthedocs.io/en/latest/\n\n.. |codecov| image:: https://codecov.io/gh/crflynn/stochastic/branch/master/graphs/badge.svg\n :target: https://codecov.io/gh/crflynn/stochastic\n\n.. |pypi| image:: https://img.shields.io/pypi/v/stochastic.svg\n :target: https://pypi.python.org/pypi/stochastic\n\n.. |pyversions| image:: https://img.shields.io/pypi/pyversions/stochastic.svg\n :target: https://pypi.python.org/pypi/stochastic\n\n\nA python package for generating realizations of stochastic processes.\n\nInstallation\n------------\n\nThe ``stochastic`` package is available on pypi and can be installed using pip\n\n.. code-block:: shell\n\n pip install stochastic\n\nDependencies\n~~~~~~~~~~~~\n\nStochastic uses ``numpy`` for many calculations and ``scipy`` for sampling\nspecific random variables.\n\nProcesses\n---------\n\nThis package offers a number of common discrete-time, continuous-time, and\nnoise process objects for generating realizations of stochastic processes as\n``numpy`` arrays.\n\nThe diffusion processes are approximated using the Euler\u2013Maruyama method.\n\nHere are the currently supported processes and their class references within\nthe package.\n\n* stochastic.processes\n\n * continuous\n\n * BesselProcess\n * BrownianBridge\n * BrownianExcursion\n * BrownianMeander\n * BrownianMotion\n * CauchyProcess\n * FractionalBrownianMotion\n * GammaProcess\n * GeometricBrownianMotion\n * InverseGaussianProcess\n * MixedPoissonProcess\n * MultifractionalBrownianMotion\n * PoissonProcess\n * SquaredBesselProcess\n * VarianceGammaProcess\n * WienerProcess\n\n * diffusion\n\n * DiffusionProcess (generalized)\n * ConstantElasticityVarianceProcess\n * CoxIngersollRossProcess\n * ExtendedVasicekProcess\n * OrnsteinUhlenbeckProcess\n * VasicekProcess\n\n * discrete\n\n * BernoulliProcess\n * ChineseRestaurantProcess\n * DirichletProcess\n * MarkovChain\n * MoranProcess\n * RandomWalk\n\n * noise\n\n * BlueNoise\n * BrownianNoise\n * ColoredNoise\n * PinkNoise\n * RedNoise\n * VioletNoise\n * WhiteNoise\n * FractionalGaussianNoise\n * GaussianNoise\n\nUsage patterns\n--------------\n\nSampling\n~~~~~~~~\n\nTo use ``stochastic``, import the process you want and instantiate with the\nrequired parameters. Every process class has a ``sample`` method for generating\nrealizations. The ``sample`` methods accept a parameter ``n`` for the quantity\nof steps in the realization, but others (Poisson, for instance) may take\nadditional parameters. Parameters can be accessed as attributes of the\ninstance.\n\n.. code-block:: python\n\n from stochastic.processes.discrete import BernoulliProcess\n\n\n bp = BernoulliProcess(p=0.6)\n s = bp.sample(16)\n success_probability = bp.p\n\n\nContinuous processes provide a default parameter, ``t``, which indicates the\nmaximum time of the process realizations. The default value is 1. The sample\nmethod will generate ``n`` equally spaced increments on the\ninterval ``[0, t]``.\n\nSampling at specific times\n~~~~~~~~~~~~~~~~~~~~~~~~~~\n\nSome continuous processes also provide a ``sample_at()`` method, in which a\nsequence of time values can be passed at which the object will generate a\nrealization. This method ignores the parameter, ``t``, specified on\ninstantiation.\n\n\n.. code-block:: python\n\n from stochastic.processes.continuous import BrownianMotion\n\n\n bm = BrownianMotion(drift=1, scale=1, t=1)\n times = [0, 3, 10, 11, 11.2, 20]\n s = bm.sample_at(times)\n\nSample times\n~~~~~~~~~~~~\n\nContinuous processes also provide a method ``times()`` which generates the time\nvalues (using ``numpy.linspace``) corresponding to a realization of ``n``\nsteps. This is particularly useful for plotting your samples.\n\n\n.. code-block:: python\n\n import matplotlib.pyplot as plt\n from stochastic.processes.continuous import FractionalBrownianMotion\n\n\n fbm = FractionalBrownianMotion(hurst=0.7, t=1)\n s = fbm.sample(32)\n times = fbm.times(32)\n\n plt.plot(times, s)\n plt.show()\n\n\nSpecifying an algorithm\n~~~~~~~~~~~~~~~~~~~~~~~\n\nSome processes provide an optional parameter ``algorithm``, in which one can\nspecify which algorithm to use to generate the realization using the\n``sample()`` or ``sample_at()`` methods. See the documentation for\nprocess-specific implementations.\n\n\n.. code-block:: python\n\n from stochastic.processes.noise import FractionalGaussianNoise\n\n\n fgn = FractionalGaussianNoise(hurst=0.6, t=1)\n s = fgn.sample(32, algorithm='hosking')\n",
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