.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "auto_examples/weibull_fit.py"
.. LINE NUMBERS ARE GIVEN BELOW.

.. only:: html

    .. note::
        :class: sphx-glr-download-link-note

        :ref:`Go to the end <sphx_glr_download_auto_examples_weibull_fit.py>`
        to download the full example code.

.. rst-class:: sphx-glr-example-title

.. _sphx_glr_auto_examples_weibull_fit.py:


Fitting Weibull Distributions
===============================

This example demonstrates how to fit Weibull parameters to a wind speed distribution
using the moments-based Weibull fitting method used by WAsP.

Lets start by fiting Weibull parameters to a known first moment (the mean wind speed), third moment, and the frequency fraction that is
greater than the mean (first moment). To fit the Weibull parameters, we will use the :py:func:`windkit.weibull.fit_weibull_wasp_m1_m3_fgtm` function.

.. GENERATED FROM PYTHON SOURCE LINES 12-25

.. code-block:: Python


    import windkit as wk
    import numpy as np
    from scipy.stats import weibull_min
    import matplotlib.pyplot as plt

    first_moment = 7.0
    third_moment = 600.0
    freq_gt_mean = 0.46

    A, k = wk.weibull.fit_weibull_wasp_m1_m3_fgtm(first_moment, third_moment, freq_gt_mean)
    print(f"Weibull A: {A:.2f}, k: {k:.2f}")





.. rst-class:: sphx-glr-script-out

 .. code-block:: none

    Weibull A: 7.87, k: 2.16




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Deriving relevant statistics from a wind speed distribution
-------------------------------------------------------------
Now, let's go back and instead start from a wind speed distribution and derive the first moment, third moment,
and frequency fraction greater than the mean. We will use a Weibull distribution with
the known parameters from above.

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.. code-block:: Python


    size = 100_000  # number of samples
    ws_samples = weibull_min.rvs(k, loc=0, scale=A, size=size, random_state=0)

    bins = np.linspace(0.0, 30.0, 31)
    centers = 0.5 * (bins[:-1] + bins[1:])
    ceils = np.ceil(centers)

    hist, bin_edges = np.histogram(ws_samples, bins=bins, density=True)








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Caculate statistics
------------------------------------------
Now, we can calculate the first moment, third moment, and the frequency fraction greater than the mean

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.. code-block:: Python


    first_moment = centers @ hist
    third_moment = (centers**3) @ hist
    cdf = np.cumsum(hist)
    freq_gt_mean = 1.0 - np.interp(first_moment, ceils, cdf)


    print(f"First Moment: {first_moment:.2f} m/s")
    print(f"Third Moment: {third_moment:.2f} m^3/s^3")
    print(f"Frequency Fraction Greater Than Mean: {freq_gt_mean:.2f}")





.. rst-class:: sphx-glr-script-out

 .. code-block:: none

    First Moment: 6.96 m/s
    Third Moment: 602.24 m^3/s^3
    Frequency Fraction Greater Than Mean: 0.46




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Fit Weibull distribution using the calculated moments

.. GENERATED FROM PYTHON SOURCE LINES 58-64

.. code-block:: Python

    A_fit, k_fit = wk.weibull.fit_weibull_wasp_m1_m3_fgtm(
        first_moment, third_moment, freq_gt_mean
    )
    print(f"Fitted Weibull A: {A_fit:.2f}, k: {k_fit:.2f}")






.. rst-class:: sphx-glr-script-out

 .. code-block:: none

    Fitted Weibull A: 7.87, k: 2.16




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Visualizing the distribution
------------------------------------------

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.. code-block:: Python


    x = np.linspace(0, 30, 1000)

    plt.bar(
        centers,
        hist,
        width=np.diff(bins),
        align="center",
        alpha=0.5,
        label="Sampled Distribution",
    )
    plt.plot(
        x,
        weibull_min.pdf(x, k_fit, loc=0, scale=A_fit),
        label=f"Weibull Fit (A={A_fit:.2f}, k={k_fit:.2f})",
        color="red",
    )
    plt.legend()
    plt.xlabel("Wind Speed (m/s)")
    plt.ylabel("Probability Density")
    plt.title("Weibull Distribution Fit")



.. image-sg:: /auto_examples/images/sphx_glr_weibull_fit_001.png
   :alt: Weibull Distribution Fit
   :srcset: /auto_examples/images/sphx_glr_weibull_fit_001.png
   :class: sphx-glr-single-img


.. rst-class:: sphx-glr-script-out

 .. code-block:: none


    Text(0.5, 1.0, 'Weibull Distribution Fit')




.. rst-class:: sphx-glr-timing

   **Total running time of the script:** (0 minutes 0.113 seconds)


.. _sphx_glr_download_auto_examples_weibull_fit.py:

.. only:: html

  .. container:: sphx-glr-footer sphx-glr-footer-example

    .. container:: sphx-glr-download sphx-glr-download-jupyter

      :download:`Download Jupyter notebook: weibull_fit.ipynb <weibull_fit.ipynb>`

    .. container:: sphx-glr-download sphx-glr-download-python

      :download:`Download Python source code: weibull_fit.py <weibull_fit.py>`

    .. container:: sphx-glr-download sphx-glr-download-zip

      :download:`Download zipped: weibull_fit.zip <weibull_fit.zip>`


.. only:: html

 .. rst-class:: sphx-glr-signature

    `Gallery generated by Sphinx-Gallery <https://sphinx-gallery.github.io>`_