.. DO NOT EDIT. .. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY. .. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE: .. "auto_data_analysis/distribution_fitting/plot_estimate_normal.py" .. LINE NUMBERS ARE GIVEN BELOW. .. only:: html .. note:: :class: sphx-glr-download-link-note Click :ref:`here ` to download the full example code .. rst-class:: sphx-glr-example-title .. _sphx_glr_auto_data_analysis_distribution_fitting_plot_estimate_normal.py: Fit a parametric distribution ============================= .. GENERATED FROM PYTHON SOURCE LINES 9-14 In this example we estimate the parameters of a distribution from a given sample. Once we are settled on a good candidate, we use the corresponding factory to fit the distribution. Each distribution factory has one or several estimators available. They are all derived from either the Maximum Likelihood method or from the method of moments (see :ref:`parametric_estimation`). .. GENERATED FROM PYTHON SOURCE LINES 16-22 .. code-block:: default import openturns as ot import openturns.viewer as viewer from matplotlib import pylab as plt ot.Log.Show(ot.Log.NONE) .. GENERATED FROM PYTHON SOURCE LINES 23-28 The Normal distribution ----------------------- The parameters are estimated by the method of moments. .. GENERATED FROM PYTHON SOURCE LINES 30-31 We consider a sample, here created from a standard normal distribution : .. GENERATED FROM PYTHON SOURCE LINES 31-33 .. code-block:: default sample = ot.Normal().getSample(1000) .. GENERATED FROM PYTHON SOURCE LINES 34-35 We can estimate a normal distribution with `ǸormalFactory` : .. GENERATED FROM PYTHON SOURCE LINES 35-37 .. code-block:: default distribution = ot.NormalFactory().build(sample) .. GENERATED FROM PYTHON SOURCE LINES 38-39 We take a look at the estimated parameters with the `getParameter` method : .. GENERATED FROM PYTHON SOURCE LINES 39-41 .. code-block:: default print(distribution.getParameter()) .. rst-class:: sphx-glr-script-out Out: .. code-block:: none [0.00320214,1.02733] .. GENERATED FROM PYTHON SOURCE LINES 42-43 We draw the fitted distribution .. GENERATED FROM PYTHON SOURCE LINES 43-47 .. code-block:: default graph = distribution.drawPDF() graph.setTitle("Fitted Normal distribution") view = viewer.View(graph) .. image-sg:: /auto_data_analysis/distribution_fitting/images/sphx_glr_plot_estimate_normal_001.png :alt: Fitted Normal distribution :srcset: /auto_data_analysis/distribution_fitting/images/sphx_glr_plot_estimate_normal_001.png :class: sphx-glr-single-img .. GENERATED FROM PYTHON SOURCE LINES 48-53 The Student distribution ------------------------ The parameters of the Student law are estimated by a mixed method of moments and reduces MLE. .. GENERATED FROM PYTHON SOURCE LINES 55-56 We generate a sample from a Student distribution with parameters :math:`\nu=5.0`, :math:`\mu = -0.5` and a scale parameter :math:`\sigma=2.0`. .. GENERATED FROM PYTHON SOURCE LINES 56-58 .. code-block:: default sample = ot.Student(5.0, -0.5, 2.0).getSample(1000) .. GENERATED FROM PYTHON SOURCE LINES 59-60 We use the factory to build an estimated distribution : .. GENERATED FROM PYTHON SOURCE LINES 60-62 .. code-block:: default distribution = ot.StudentFactory().build(sample) .. GENERATED FROM PYTHON SOURCE LINES 63-64 We can obtain the estimated parameters with the `getParameter` method : .. GENERATED FROM PYTHON SOURCE LINES 64-67 .. code-block:: default print(distribution.getParameter()) .. rst-class:: sphx-glr-script-out Out: .. code-block:: none [3.65576,-0.515215,1.84614] .. GENERATED FROM PYTHON SOURCE LINES 68-69 Draw fitted distribution .. GENERATED FROM PYTHON SOURCE LINES 69-73 .. code-block:: default graph = distribution.drawPDF() graph.setTitle("Fitted Student distribution") view = viewer.View(graph) .. image-sg:: /auto_data_analysis/distribution_fitting/images/sphx_glr_plot_estimate_normal_002.png :alt: Fitted Student distribution :srcset: /auto_data_analysis/distribution_fitting/images/sphx_glr_plot_estimate_normal_002.png :class: sphx-glr-single-img .. GENERATED FROM PYTHON SOURCE LINES 74-79 The Pareto distribution ----------------------- By default the parameters of the Pareto distribution are estimated by least squares. .. GENERATED FROM PYTHON SOURCE LINES 81-82 We use a sample from a Pareto distribution with a scale parameter :math:`\beta=1.0`, a shape parameter :math:`\alpha > 1.0` and a location parameter :math:`\gamma = 0.0`. .. GENERATED FROM PYTHON SOURCE LINES 82-84 .. code-block:: default sample = ot.Pareto(1.0, 1.0, 0.0).getSample(1000) .. GENERATED FROM PYTHON SOURCE LINES 85-86 Draw fitted distribution .. GENERATED FROM PYTHON SOURCE LINES 86-96 .. code-block:: default distribution = ot.ParetoFactory().build(sample) print(distribution.getParameter()) graph = distribution.drawPDF() graph.setTitle("Fitted Pareto distribution") view = viewer.View(graph) plt.show() .. image-sg:: /auto_data_analysis/distribution_fitting/images/sphx_glr_plot_estimate_normal_003.png :alt: Fitted Pareto distribution :srcset: /auto_data_analysis/distribution_fitting/images/sphx_glr_plot_estimate_normal_003.png :class: sphx-glr-single-img .. rst-class:: sphx-glr-script-out Out: .. code-block:: none [0.787856,0.944192,0.246677] .. rst-class:: sphx-glr-timing **Total running time of the script:** ( 0 minutes 0.260 seconds) .. _sphx_glr_download_auto_data_analysis_distribution_fitting_plot_estimate_normal.py: .. only :: html .. container:: sphx-glr-footer :class: sphx-glr-footer-example .. container:: sphx-glr-download sphx-glr-download-python :download:`Download Python source code: plot_estimate_normal.py ` .. container:: sphx-glr-download sphx-glr-download-jupyter :download:`Download Jupyter notebook: plot_estimate_normal.ipynb ` .. only:: html .. rst-class:: sphx-glr-signature `Gallery generated by Sphinx-Gallery `_