uki" ,ddlZddlmZddlmZddlmZddlm Z ddl m Z m Z  dde de d e d e d e f d Z dde de d e d e d e f d Z dde de d e d e d e f dZ dde de d e d e d e f dZ dde de d e d e d e f dZ dde de d e d e d e f dZ dde de d e d e d e f dZy)N)lax)numpy)_const)promote_args_inexact)Array ArrayLikexblocscalereturnc Ltd||||\}}}}t|d}tjtj|||}tj tj||}tj tj|tjtj||tj |}tjtj|tj||tj |S)a8Pareto log probability distribution function. JAX implementation of :obj:`scipy.stats.pareto` ``logpdf``. The Pareto probability density function is given by .. math:: f(x, b) = \begin{cases} bx^{-(b+1)} & x \ge 1\\ 0 & x < 1 \end{cases} and is defined for :math:`b > 0`. Args: x: arraylike, value at which to evaluate the PDF b: arraylike, distribution shape parameter loc: arraylike, distribution offset parameter scale: arraylike, distribution scale parameter Returns: array of logpdf values. See Also: - :func:`jax.scipy.stats.pareto.logcdf` - :func:`jax.scipy.stats.pareto.logsf` - :func:`jax.scipy.stats.pareto.cdf` - :func:`jax.scipy.stats.pareto.pdf` - :func:`jax.scipy.stats.pareto.ppf` - :func:`jax.scipy.stats.pareto.sf` z pareto.logpdf)r _lax_constrdivsublognegaddmuljnpwhereltnpinf)r r r r onescaled_xnormalize_term log_probss V/home/cdr/jupyterlab/.venv/lib/python3.12/site-packages/jax/_src/scipy/stats/pareto.pylogpdfr!sF*/1aeL!QU1a# WWSWWQ_e ,(773775!,-.ggGGNCGGCGGAsOSWWX5FGH) 366!SWWS%01BFF7I FFcDtjt||||S)a1Pareto probability distribution function. JAX implementation of :obj:`scipy.stats.pareto` ``pdf``. The Pareto probability density function is given by .. math:: f(x, b) = \begin{cases} bx^{-(b+1)} & x \ge 1\\ 0 & x < 1 \end{cases} and is defined for :math:`b > 0`. Args: x: arraylike, value at which to evaluate the PDF b: arraylike, distribution shape parameter loc: arraylike, distribution offset parameter scale: arraylike, distribution scale parameter Returns: array of pdf values. See Also: - :func:`jax.scipy.stats.pareto.logcdf` - :func:`jax.scipy.stats.pareto.logpdf` - :func:`jax.scipy.stats.pareto.logsf` - :func:`jax.scipy.stats.pareto.cdf` - :func:`jax.scipy.stats.pareto.ppf` - :func:`jax.scipy.stats.pareto.sf` )rexpr!r r r r s r pdfr&FsF 1c5) **r"c td||||\}}}}t|d}t|d}tjtj|||}tj|tj |tj |}tjtj|tj||||S)a3Pareto cumulative distribution function. JAX implementation of :obj:`scipy.stats.pareto` ``cdf``. The Pareto cumulative distribution function is given by .. math:: F(x, b) = \begin{cases} 1 - x^{-b} & x \ge 1\\ 0 & x < 1 \end{cases} and is defined for :math:`b > 0`. Args: x: arraylike, value at which to evaluate the CDF b: arraylike, distribution shape parameter loc: arraylike, distribution offset parameter scale: arraylike, distribution scale parameter Returns: array of CDF values. See Also: - :func:`jax.scipy.stats.pareto.logcdf` - :func:`jax.scipy.stats.pareto.logpdf` - :func:`jax.scipy.stats.pareto.logsf` - :func:`jax.scipy.stats.pareto.pdf` - :func:`jax.scipy.stats.pareto.ppf` - :func:`jax.scipy.stats.pareto.sf` z pareto.cdfrr) rrrrrpowrrrrr)r r r r rzerorcdfs r r*r*lsF*,1c5I!QU1a# Aq $ WWSWWQ_e ,( SWWXswwqz23# 366!SWWS%014 ==r"c td||||\}}}}tjtj|||}tjtj tj |tj |}tjtj|tj||tj |S)a:Pareto log cumulative distribution function. JAX implementation of :obj:`scipy.stats.pareto` ``logcdf``. The Pareto cumulative distribution function is given by .. math:: F(x, b) = \begin{cases} 1 - x^{-b} & x \ge 1\\ 0 & x < 1 \end{cases} and is defined for :math:`b > 0`. Args: x: arraylike, value at which to evaluate the CDF b: arraylike, distribution shape parameter loc: arraylike, distribution offset parameter scale: arraylike, distribution scale parameter Returns: array of logCDF values. See Also: - :func:`jax.scipy.stats.pareto.logpdf` - :func:`jax.scipy.stats.pareto.logsf` - :func:`jax.scipy.stats.pareto.cdf` - :func:`jax.scipy.stats.pareto.pdf` - :func:`jax.scipy.stats.pareto.ppf` - :func:`jax.scipy.stats.pareto.sf` z pareto.logcdf) rrrrlog1prr(rrrrrr)r r r r r logcdf_vals r logcdfr.sF*/1aeL!QU WWSWWQ_e ,(yy3771:!>?@* 366!SWWS%01BFF7J GGr"c td||||\}}}}t|d}tjtj|||}tj tj |tj|}tjtj|tj||||S)a5Pareto log survival function. JAX implementation of :obj:`scipy.stats.pareto` ``logsf``. The Pareto survival function is given by .. math:: S(x, b) = \begin{cases} x^{-b} & x \ge 1\\ 1 & x < 1 \end{cases} and is defined for :math:`b > 0`. Args: x: arraylike, value at which to evaluate the survival function b: arraylike, distribution shape parameter loc: arraylike, distribution offset parameter scale: arraylike, distribution scale parameter Returns: array of log survival function values. See Also: - :func:`jax.scipy.stats.pareto.logcdf` - :func:`jax.scipy.stats.pareto.logpdf` - :func:`jax.scipy.stats.pareto.cdf` - :func:`jax.scipy.stats.pareto.pdf` - :func:`jax.scipy.stats.pareto.ppf` - :func:`jax.scipy.stats.pareto.sf` z pareto.logsfr) rrrrrrrrrrrr)r r r r r)r logsf_vals r logsfr1sF*.!QUK!QU Aq $ WWSWWQ_e ,(ggcgga!234) 366!SWWS%014 CCr"cDtjt||||S)a-Pareto survival function. JAX implementation of :obj:`scipy.stats.pareto` ``sf``. The Pareto survival function is given by .. math:: S(x, b) = \begin{cases} x^{-b} & x \ge 1\\ 1 & x < 1 \end{cases} and is defined for :math:`b > 0`. Args: x: arraylike, value at which to evaluate the survival function b: arraylike, distribution shape parameter loc: arraylike, distribution offset parameter scale: arraylike, distribution scale parameter Returns: array of survival function values. See Also: - :func:`jax.scipy.stats.pareto.logcdf` - :func:`jax.scipy.stats.pareto.logpdf` - :func:`jax.scipy.stats.pareto.logsf` - :func:`jax.scipy.stats.pareto.cdf` - :func:`jax.scipy.stats.pareto.pdf` - :func:`jax.scipy.stats.pareto.ppf` )rr$r1r%s r sfr3sF q!S%( ))r"qctd||||\}}}}t|d}tj|tj|tj tj ||tjtj||}tjtj||dkz|dkDztj|S)aPareto percent point function (inverse CDF). JAX implementation of :obj:`scipy.stats.pareto` ``ppf``. The Pareto percent point function is the inverse of the Pareto CDF, and is given by .. math:: F^{-1}(q, b) = \begin{cases} (1 - q)^{-1/b} & 0 \le q < 1\\ \text{NaN} & \text{otherwise} \end{cases} and is defined for :math:`b > 0`. Args: q: arraylike, value at which to evaluate the inverse CDF b: arraylike, distribution shape parameter loc: arraylike, distribution offset parameter scale: arraylike, distribution scale parameter Returns: array of percent point function values. See Also: - :func:`jax.scipy.stats.pareto.logcdf` - :func:`jax.scipy.stats.pareto.logpdf` - :func:`jax.scipy.stats.pareto.logsf` - :func:`jax.scipy.stats.pareto.cdf` - :func:`jax.scipy.stats.pareto.pdf` - :func:`jax.scipy.stats.pareto.sf` z pareto.ppfrr)rrrrrr(rrrrrisnanrnan)r4r r r rppf_vals r ppfr9sH*,1c5I!QU1a# GGQa1IJ K ' 399Q<1q5)QU3RVVW EEr")rr)rrjax._srcrrjax._src.lax.laxrrjax._src.numpy.utilrjax._src.typingrrr!r&r*r.r1r3r9r"r r?s !14,FG*G*G*G#,*G9B*G *G\FG#+#+#+#,#+9B#+ #+NFG(>(>(>#,(>9B(> (>XFG&H&H&H#,&H9B&H &HTFG'D'D'D#,'D9B'D 'DVFG#*#*#*#,#*9B#* #*NFG)F)F)F#,)F9B)F )Fr"