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Editing: _tukeylambda_stats.cpython-311.pyc
� d�c� � �� � d dl Zd dl mZ d dlmZ g d�Zg d�Z eeddd� � � Z eeddd� � � Zd� Z g d�Z g d �Z ee ddd� � � Z ee ddd� � � Z d � ZdS ) � N)�poly1d)�beta)g�Sb�Q @g�o�|-a�?g_3 L�/�g�|�A"�?gC�U�G��)� �?g<��*x @g�� y��@g`B{d�A�?g-��~���?���c �Z � t j | � � } | j }t j | � � � t j � � } d}| dk }| dk }t j | � � |k }||z |z }| | }| | }t j | � � } t j | |< t j | |< |j dk r"t |� � t |� � z | |< |j dk r.d|dz z ddd|z z z t |dz |dz � � z z | |< || _ | S )a� Variance of the Tukey Lambda distribution. Parameters ---------- lam : array_like The lambda values at which to compute the variance. Returns ------- v : ndarray The variance. For lam < -0.5, the variance is not defined, so np.nan is returned. For lam = 0.5, np.inf is returned. Notes ----- In an interval around lambda=0, this function uses the [4,4] Pade approximation to compute the variance. Otherwise it uses the standard formula (https://en.wikipedia.org/wiki/Tukey_lambda_distribution). The Pade approximation is used because the standard formula has a removable discontinuity at lambda = 0, and does not produce accurate numerical results near lambda = 0. g333333�?g �r g @� r � )�np�asarray�shape� atleast_1d�astype�float64�abs� empty_like�nan�inf�size�_tukeylambda_var_p�_tukeylambda_var_qr ) �lam�shp� threshold�low_mask� neghalf_mask� small_mask�reg_mask�small�reg�vs �@/usr/lib/python3/dist-packages/scipy/stats/_tukeylambda_stats.py�tukeylambda_variancer" + s1 � �. �*�S�/�/�C� �)�C� �-�� � � #� #�B�J� /� /�C� �I� �T�z�H��$�;�L������y�(�J��L�(�:�5�6�H� � �O�E� �h�-�C� � �c���A��&�A�h�K��f�A�l�O� �z�A�~�~�*�5�1�1�4F�u�4M�4M�M��*� � �x�!�|�|��S�!�V�|��s�Q��W�}�(=�&*�3��7�C�!�G�&<�&<�)=� >��(� ��A�G� �H� )g333333�?g6|���i�ge��SH�6�gѐ환^�?g˝)kPd@)r g?�ݻA� @gID@��)@g���Pr��?g`2��fQ�c �� � t j | � � } | j }t j | � � � t j � � } d}| dk }| dk }t j | � � |k }||z |z }| | }| | }t j | � � } t j | |< t j | |< |j dk r"t |� � t |� � z | |< |j dk r{dd|z dz z dt d|z dz |dz � � z z dt d|z dz d|z dz � � z z } ddd|z dz z t |dz |dz � � z dz z } | | z dz | |< || _ | S ) aR Kurtosis of the Tukey Lambda distribution. Parameters ---------- lam : array_like The lambda values at which to compute the variance. Returns ------- v : ndarray The variance. For lam < -0.25, the variance is not defined, so np.nan is returned. For lam = 0.25, np.inf is returned. g)\��(�?g пr r � r � r )r r r r r r r r r r r �_tukeylambda_kurt_p�_tukeylambda_kurt_qr ) r r r r � negqrtr_maskr r r r �k�numer�denoms r! �tukeylambda_kurtosisr- � s� � � �*�S�/�/�C� �)�C� �-�� � � #� #�B�J� /� /�C� �I� �U�{�H��%�<�L������y�(�J��L�(�:�5�6�H� � �O�E� �h�-�C� � �c���A��&�A�h�K��f�A�l�O� �z�A�~�~�+�E�2�2�5H��5O�5O�O��*� � �x�!�|�|���C��!� �$�q�4��C��!� �S�1�W�+E�+E�'E�E��T�!�c�'�A�+�q�3�w��{�3�3�3�4���S�!�c�'�A�+�&��c�A�g�s�Q�w�)?�)?�?�!�C�C���e�m�a�'��(� � �A�G� �Hr# )�numpyr r � scipy.specialr �_tukeylambda_var_pc�_tukeylambda_var_qcr r r" �_tukeylambda_kurt_pc�_tukeylambda_kurt_qcr' r( r- � r# r! �<module>r5 s �� � � � � � � � � � � � � � � � �8-� -� -� �?� ?� ?� � �V� /���"�� 5�6�6� ��V� /���"�� 5�6�6� �9 � 9 � 9 �z?� ?� ?� �A� A� A� � �f� 1�$�$�B�$� 7�8�8� � �f� 1�$�$�B�$� 7�8�8� �4 � 4 � 4 � 4 � 4 r#
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