o Eb@sddlZddlmZddlmZgdZgdZeedddZeedddZddZ gd Z gd Z ee dddZ ee dddZ d d ZdS) N)poly1d)beta)gSbQ @go|-a?g_3 L/g|A"?gCUG)?g<*x @gy@g`B{dA?g-~?c Cst|}|j}t|tj}d}|dk}|dk}t||k}||B|B}||}||}t|} tj| |<tj | |<|j dkrOt |t || |<|j dkrmd|dddd|t |d|d| |<|| _| S)aVariance 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?grg@r)npasarrayshape atleast_1dastypefloat64abs empty_likenaninfsize_tukeylambda_var_p_tukeylambda_var_qr) lamshp thresholdlow_maskZ neghalf_mask small_maskreg_masksmallregvr@/usr/lib/python3/dist-packages/scipy/stats/_tukeylambda_stats.pytukeylambda_variance+s*       r )g333333?g6|igeSH6gѐ환^?g˝)kPd@)rg?ݻA@gID@)@gPr?g`2fQc Cs4t|}|j}t|tj}d}|dk}|dk}t||k}||B|B}||}||}t|} tj| |<tj | |<|j dkrOt |t || |<|j dkrdd|ddt d|d|ddt d|dd|d} ddd|dt |d|dd} | | d| |<|| _| S) aRKurtosis 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)\(?gпrrrr)rr r r r r rrrrr_tukeylambda_kurt_p_tukeylambda_kurt_qr) rrrrZ negqrtr_maskrrrrkZnumerZdenomrrrtukeylambda_kurtosiss.      (*r&)ZnumpyrrZ scipy.specialrZ_tukeylambda_var_pcZ_tukeylambda_var_qcrrr Z_tukeylambda_kurt_pcZ_tukeylambda_kurt_qcr#r$r&rrrrs  ]