9jPSSKJr SSKJr SSKJr S\4SjrS\4Sjr S\4Sjr S\4Sjr S\4S jr S\4S jr S S\4S jrS,S jrSS S\4SjrS,SjrSS S\4SjrSS S\4SjrSS S\4SjrS,SjrS\4SjrSSSS\4SjrSS S\4SjrS\4SjrS\4SjrS\4SjrS-SjrS\4SjrS S\4S jrS\4S!jrS\4S"jr S\4S#jr!S\4S$jr"S\4S%jr#S\4S&jr$SS S\4S'jr%S\4S(jr&S\4S)jr'S\4S*jr(S\4S+jr)g).) annotations) _generator)_utilNcP[R"5nURXX#5$)aBeta distribution. Returns an array of samples drawn from the beta distribution. Its probability density function is defined as .. math:: f(x) = \frac{x^{\alpha-1}(1-x)^{\beta-1}}{B(\alpha,\beta)}. Args: a (float): Parameter of the beta distribution :math:`\alpha`. b (float): Parameter of the beta distribution :math:`\beta`. size (int or tuple of ints): The shape of the array. If ``None``, a zero-dimensional array is generated. dtype: Data type specifier. Only :class:`numpy.float32` and :class:`numpy.float64` types are allowed. Returns: cupy.ndarray: Samples drawn from the beta distribution. .. seealso:: :func:`numpy.random.beta` )rget_random_statebeta)absizedtyperss T/home/wildlama/miniconda3/lib/python3.13/site-packages/cupy/random/_distributions.pyrr s#.  $ $ &B 771 %%cP[R"5nURXX#5$)aBinomial distribution. Returns an array of samples drawn from the binomial distribution. Its probability mass function is defined as .. math:: f(x) = \binom{n}{x}p^x(1-p)^{n-x}. Args: n (int): Trial number of the binomial distribution. p (float): Success probability of the binomial distribution. size (int or tuple of ints): The shape of the array. If ``None``, a zero-dimensional array is generated. dtype: Data type specifier. Only :class:`numpy.int32` and :class:`numpy.int64` types are allowed. Returns: cupy.ndarray: Samples drawn from the binomial distribution. .. seealso:: :func:`numpy.random.binomial` )rrbinomialnpr r r s rrr%s#.  $ $ &B ;;qT ))rcP[R"5nURXU5$)aChi-square distribution. Returns an array of samples drawn from the chi-square distribution. Its probability density function is defined as .. math:: f(x) = \frac{(1/2)^{k/2}}{\Gamma(k/2)}x^{k/2-1}e^{-x/2}. Args: df (int or array_like of ints): Degree of freedom :math:`k`. size (int or tuple of ints): The shape of the array. If ``None``, a zero-dimensional array is generated. dtype: Data type specifier. Only :class:`numpy.float32` and :class:`numpy.float64` types are allowed. Returns: cupy.ndarray: Samples drawn from the chi-square distribution. .. seealso:: :func:`numpy.random.chisquare` )rr chisquaredfr r r s rrr@s#,  $ $ &B <<% ((rcP[R"5nURXU5$)aDirichlet distribution. Returns an array of samples drawn from the dirichlet distribution. Its probability density function is defined as .. math:: f(x) = \frac{\Gamma(\sum_{i=1}^K\alpha_i)} {\prod_{i=1}^{K}\Gamma(\alpha_i)} \prod_{i=1}^Kx_i^{\alpha_i-1}. Args: alpha (array): Parameters of the dirichlet distribution :math:`\alpha`. size (int or tuple of ints): The shape of the array. If ``None``, a zero-dimensional array is generated. dtype: Data type specifier. Only :class:`numpy.float32` and :class:`numpy.float64` types are allowed. Returns: cupy.ndarray: Samples drawn from the dirichlet distribution. .. seealso:: :func:`numpy.random.dirichlet` )rr dirichlet)alphar r r s rrrZs#2  $ $ &B <<U ++rcP[R"5nURXU5$)aExponential distribution. Returns an array of samples drawn from the exponential distribution. Its probability density function is defined as .. math:: f(x) = \frac{1}{\beta}\exp (-\frac{x}{\beta}). Args: scale (float or array_like of floats): The scale parameter :math:`\beta`. size (int or tuple of ints): The shape of the array. If ``None``, a zero-dimensional array is generated. dtype: Data type specifier. Only :class:`numpy.float32` and :class:`numpy.float64` types are allowed. Returns: cupy.ndarray: Samples drawn from the exponential distribution. .. seealso:: :func:`numpy.random.exponential` )rr exponentialscaler r r s rrrws#.  $ $ &B >>%u --rcP[R"5nURXX#5$)a|F distribution. Returns an array of samples drawn from the f distribution. Its probability density function is defined as .. math:: f(x) = \frac{1}{B(\frac{d_1}{2},\frac{d_2}{2})} \left(\frac{d_1}{d_2}\right)^{\frac{d_1}{2}} x^{\frac{d_1}{2}-1} \left(1+\frac{d_1}{d_2}x\right) ^{-\frac{d_1+d_2}{2}}. Args: dfnum (float or array_like of floats): Parameter of the f distribution :math:`d_1`. dfden (float or array_like of floats): Parameter of the f distribution :math:`d_2`. size (int or tuple of ints): The shape of the array. If ``None``, a zero-dimensional array is generated. dtype: Data type specifier. Only :class:`numpy.float32` and :class:`numpy.float64` types are allowed. Returns: cupy.ndarray: Samples drawn from the f distribution. .. seealso:: :func:`numpy.random.f` )rrf)dfnumdfdenr r r s rr!r!s#:  $ $ &B 44d **r?cP[R"5nURXX#5$)aGamma distribution. Returns an array of samples drawn from the gamma distribution. Its probability density function is defined as .. math:: f(x) = \frac{1}{\Gamma(k)\theta^k}x^{k-1}e^{-x/\theta}. Args: shape (array): Parameter of the gamma distribution :math:`k`. scale (array): Parameter of the gamma distribution :math:`\theta` size (int or tuple of ints): The shape of the array. If ``None``, a zero-dimensional array is generated. dtype: Data type specifier. Only :class:`numpy.float32` and :class:`numpy.float64` types are allowed. Returns:cupy.ndarray: Samples drawn from the gamma distribution. .. seealso:: :func:`numpy.random.gamma` )rrgamma)shaperr r r s rr&r&s#,  $ $ &B 88E$ ..rcP[R"5nURXU5$)aTGeometric distribution. Returns an array of samples drawn from the geometric distribution. Its probability mass function is defined as .. math:: f(x) = p(1-p)^{k-1}. Args: p (float): Success probability of the geometric distribution. size (int or tuple of ints): The shape of the array. If ``None``, a zero-dimensional array is generated. dtype: Data type specifier. Only :class:`numpy.int32` and :class:`numpy.int64` types are allowed. Returns: cupy.ndarray: Samples drawn from the geometric distribution. .. seealso:: :func:`numpy.random.geometric` )rr geometricrr r r s rr)r)s#,  $ $ &B << ''rgcP[R"5nURXX#5$)aReturns an array of samples drawn from a Gumbel distribution. The samples are drawn from a Gumbel distribution with location ``loc`` and scale ``scale``. Its probability density function is defined as .. math:: f(x) = \frac{1}{\eta} \exp\left\{ - \frac{x - \mu}{\eta} \right\} \exp\left[-\exp\left\{-\frac{x - \mu}{\eta} \right\}\right], where :math:`\mu` is ``loc`` and :math:`\eta` is ``scale``. Args: loc (float): The location of the mode :math:`\mu`. scale (float): The scale parameter :math:`\eta`. size (int or tuple of ints): The shape of the array. If ``None``, a zero-dimensional array is generated. dtype: Data type specifier. Only :class:`numpy.float32` and :class:`numpy.float64` types are allowed. Returns: cupy.ndarray: Samples drawn from the Gumbel distribution. .. seealso:: :func:`numpy.random.gumbel` )rrgumbellocrr r r s rr,r,s#:  $ $ &B 99S --rcR[R"5nURXX#U5$)ahypergeometric distribution. Returns an array of samples drawn from the hypergeometric distribution. Its probability mass function is defined as .. math:: f(x) = \frac{\binom{m}{n}\binom{N-m}{n-x}}{\binom{N}{n}}. Args: ngood (int or array_like of ints): Parameter of the hypergeometric distribution :math:`n`. nbad (int or array_like of ints): Parameter of the hypergeometric distribution :math:`m`. nsample (int or array_like of ints): Parameter of the hypergeometric distribution :math:`N`. size (int or tuple of ints): The shape of the array. If ``None``, a zero-dimensional array is generated. dtype: Data type specifier. Only :class:`numpy.int32` and :class:`numpy.int64` types are allowed. Returns: cupy.ndarray: Samples drawn from the hypergeometric distribution. .. seealso:: :func:`numpy.random.hypergeometric` )rrhypergeometric)ngoodnbadnsampler r r s rr0r0s'6  $ $ &B  U' ??rcP[R"5nURXX#5$)aLogistic distribution. Returns an array of samples drawn from the logistic distribution. Its probability density function is defined as .. math:: f(x) = \frac{e^{-(x-\mu)/s}}{s(1+e^{-(x-\mu)/s})^2}. Args: loc (float): The location of the mode :math:`\mu`. scale (float): The scale parameter :math:`s`. size (int or tuple of ints): The shape of the array. If ``None``, a zero-dimensional array is generated. dtype: Data type specifier. Only :class:`numpy.float32` and :class:`numpy.float64` types are allowed. Returns: cupy.ndarray: Samples drawn from the logistic distribution. .. seealso:: :func:`numpy.random.logistic` )rrlogisticr-s rr5r5's#.  $ $ &B ;;s4 //rcP[R"5nURXX#5$)aLaplace distribution. Returns an array of samples drawn from the laplace distribution. Its probability density function is defined as .. math:: f(x) = \frac{1}{2b}\exp\left(-\frac{|x-\mu|}{b}\right). Args: loc (float): The location of the mode :math:`\mu`. scale (float): The scale parameter :math:`b`. size (int or tuple of ints): The shape of the array. If ``None``, a zero-dimensional array is generated. dtype: Data type specifier. Only :class:`numpy.float32` and :class:`numpy.float64` types are allowed. Returns: cupy.ndarray: Samples drawn from the laplace distribution. .. seealso:: :func:`numpy.random.laplace` )rrlaplacer-s rr7r7Bs#.  $ $ &B ::c$ ..rcL[R"5nURXX#S9$)aReturns an array of samples drawn from a log normal distribution. The samples are natural log of samples drawn from a normal distribution with mean ``mean`` and deviation ``sigma``. Args: mean (float): Mean of the normal distribution. sigma (float): Standard deviation of the normal distribution. size (int or tuple of ints): The shape of the array. If ``None``, a zero-dimensional array is generated. dtype: Data type specifier. Only :class:`numpy.float32` and :class:`numpy.float64` types are allowed. Returns: cupy.ndarray: Samples drawn from the log normal distribution. .. seealso:: :func:`numpy.random.lognormal` r r )rr lognormal)meansigmar r r s rr:r:]s%(  $ $ &B <<$< <r>us%,  $ $ &B <<E< 22rcL[R"5nURXX#S9$)aNegative binomial distribution. Returns an array of samples drawn from the negative binomial distribution. Its probability mass function is defined as .. math:: f(x) = \binom{x + n - 1}{n - 1}p^n(1-p)^{x}. Args: n (int): Parameter of the negative binomial distribution :math:`n`. p (float): Parameter of the negative binomial distribution :math:`p`. size (int or tuple of ints): The shape of the array. If ``None``, a zero-dimensional array is generated. dtype: Data type specifier. Only :class:`numpy.int32` and :class:`numpy.int64` types are allowed. Returns: cupy.ndarray: Samples drawn from the negative binomial distribution. .. seealso:: :func:`numpy.random.negative_binomial` r9)rrnegative_binomialrs rr@r@s(.  $ $ &B  4  ==rignoreg:0yE>choleskyc [R"S5 [R"5nUR XX#XEU5$)a Multivariate normal distribution. Returns an array of samples drawn from the multivariate normal distribution. Its probability density function is defined as .. math:: f(x) = \frac{1}{(2\pi|\Sigma|)^(n/2)} \exp\left(-\frac{1}{2} (x-\mu)^{\top}\Sigma^{-1}(x-\mu)\right). Args: mean (1-D array_like, of length N): Mean of the multivariate normal distribution :math:`\mu`. cov (2-D array_like, of shape (N, N)): Covariance matrix :math:`\Sigma` of the multivariate normal distribution. It must be symmetric and positive-semidefinite for proper sampling. size (int or tuple of ints): The shape of the array. If ``None``, a zero-dimensional array is generated. check_valid ('warn', 'raise', 'ignore'): Behavior when the covariance matrix is not positive semidefinite. tol (float): Tolerance when checking the singular values in covariance matrix. method : { 'cholesky', 'eigh', 'svd'}, optional The cov input is used to compute a factor matrix A such that ``A @ A.T = cov``. This argument is used to select the method used to compute the factor matrix A. The default method 'cholesky' is the fastest, while 'svd' is the slowest but more robust than the fastest method. The method `eigh` uses eigen decomposition to compute A and is faster than svd but slower than cholesky. dtype: Data type specifier. Only :class:`numpy.float32` and :class:`numpy.float64` types are allowed. Returns: cupy.ndarray: Samples drawn from the multivariate normal distribution. .. note:: Default `method` is set to fastest, 'cholesky', unlike numpy which defaults to 'svd'. Cholesky decomposition in CuPy will fail silently if the input covariance matrix is not positive definite and give invalid results, unlike in numpy, where an invalid covariance matrix will raise an exception. Setting `check_valid` to 'raise' will replicate numpy behavior by checking the input, but will also force device synchronization. If validity of input is unknown, setting `method` to 'einh' or 'svd' and `check_valid` to 'warn' will use cholesky decomposition for positive definite matrices, and fallback to the specified `method` for other matrices (i.e., not positive semi-definite), and will warn if decomposition is suspect. .. seealso:: :func:`numpy.random.multivariate_normal` zcupy.random.multivariate_normal)r experimentalrrmultivariate_normal)r;covr check_validtolmethodr r s rrErEs>h 89  $ $ &B ! ! 4c5 ::rcP[R"5nURXX#5$)a1Returns an array of normally distributed samples. Args: loc (float or array_like of floats): Mean of the normal distribution. scale (float or array_like of floats): Standard deviation of the normal distribution. size (int or tuple of ints): The shape of the array. If ``None``, a zero-dimensional array is generated. dtype: Data type specifier. Only :class:`numpy.float32` and :class:`numpy.float64` types are allowed. Returns: cupy.ndarray: Normally distributed samples. .. seealso:: :func:`numpy.random.normal` )rrnormalr-s rrKrKs#$  $ $ &B 99S --rcP[R"5nURXU5$)aPareto II or Lomax distribution. Returns an array of samples drawn from the Pareto II distribution. Its probability density function is defined as .. math:: f(x) = \alpha(1+x)^{-(\alpha+1)}. Args: a (float or array_like of floats): Parameter of the Pareto II distribution :math:`\alpha`. size (int or tuple of ints): The shape of the array. If ``None``, this function generate an array whose shape is `a.shape`. dtype: Data type specifier. Only :class:`numpy.float32` and :class:`numpy.float64` types are allowed. Returns: cupy.ndarray: Samples drawn from the Pareto II distribution. .. seealso:: :func:`numpy.random.pareto` )rrparetor r r r s rrMrMs#,  $ $ &B 99Qe $$rcL[R"5nURXX#S9$)aNoncentral chisquare distribution. Returns an array of samples drawn from the noncentral chisquare distribution. Its probability density function is defined as .. math:: f(x) = \frac{1}{2}e^{-(x+\lambda)/2} \ \left(\frac{x}{\lambda}\right)^{k/4 - 1/2} \ I_{k/2 - 1}(\sqrt{\lambda x}), where :math:`I` is the modified Bessel function of the first kind. Args: df (float): Parameter of the noncentral chisquare distribution :math:`k`. nonc (float): Parameter of the noncentral chisquare distribution :math:`\lambda`. size (int or tuple of ints): The shape of the array. If ``None``, a zero-dimensional array is generated. dtype: Data type specifier. Only :class:`numpy.float32` and :class:`numpy.float64` types are allowed. Returns: cupy.ndarray: Samples drawn from the noncentral chisquare distribution. .. seealso:: :func:`numpy.random.noncentral_chisquare` r9)rrnoncentral_chisquare)rnoncr r r s rrPrPs(:  $ $ &B " "2$ " DDrcN[R"5nURXX#US9$)aNoncentral F distribution. Returns an array of samples drawn from the noncentral F distribution. Reference: https://en.wikipedia.org/wiki/Noncentral_F-distribution Args: dfnum (float): Parameter of the noncentral F distribution. dfden (float): Parameter of the noncentral F distribution. nonc (float): Parameter of the noncentral F distribution. size (int or tuple of ints): The shape of the array. If ``None``, a zero-dimensional array is generated. dtype: Data type specifier. Only :class:`numpy.float32` and :class:`numpy.float64` types are allowed. Returns: cupy.ndarray: Samples drawn from the noncentral F distribution. .. seealso:: :func:`numpy.random.noncentral_f` r9)rr noncentral_f)r"r#rQr r r s rrSrS5s'.  $ $ &B ??5? FFrcP[R"5nURXU5$)aPoisson distribution. Returns an array of samples drawn from the poisson distribution. Its probability mass function is defined as .. math:: f(x) = \frac{\lambda^xe^{-\lambda}}{k!}. Args: lam (array_like of floats): Parameter of the poisson distribution :math:`\lambda`. size (int or tuple of ints): The shape of the array. If ``None``, this function generate an array whose shape is `lam.shape`. dtype: Data type specifier. Only :class:`numpy.int32` and :class:`numpy.int64` types are allowed. Returns: cupy.ndarray: Samples drawn from the poisson distribution. .. seealso:: :func:`numpy.random.poisson` )rrpoisson)lamr r r s rrUrUPs#,  $ $ &B ::c ''rcP[R"5nURXU5$)aBPower distribution. Returns an array of samples drawn from the power distribution. Its probability density function is defined as .. math:: f(x) = ax^{a-1}. Args: a (float): Parameter of the power distribution :math:`a`. size (int or tuple of ints): The shape of the array. If ``None``, a zero-dimensional array is generated. dtype: Data type specifier. Only :class:`numpy.float32` and :class:`numpy.float64` types are allowed. Returns: cupy.ndarray: Samples drawn from the power distribution. .. seealso:: :func:`numpy.random.power` )rrpowerrNs rrXrXjs#,  $ $ &B 88AU ##rcP[R"5nURXU5$)aRayleigh distribution. Returns an array of samples drawn from the rayleigh distribution. Its probability density function is defined as .. math:: f(x) = \frac{x}{\sigma^2}e^{\frac{-x^2}{2-\sigma^2}}, x \ge 0. Args: scale (array): Parameter of the rayleigh distribution :math:`\sigma`. size (int or tuple of ints): The shape of the array. If ``None``, a zero-dimensional array is generated. dtype: Data type specifier. Only :class:`numpy.float32` and :class:`numpy.float64` types are allowed. Returns: cupy.ndarray: Samples drawn from the rayleigh distribution. .. seealso:: :func:`numpy.random.rayleigh` )rrrayleighrs rrZrZs#*  $ $ &B ;;uE **rcN[R"5nURX5$)a8Standard cauchy distribution. Returns an array of samples drawn from the standard cauchy distribution. Its probability density function is defined as .. math:: f(x) = \frac{1}{\pi(1+x^2)}. Args: size (int or tuple of ints): The shape of the array. If ``None``, a zero-dimensional array is generated. dtype: Data type specifier. Only :class:`numpy.float32` and :class:`numpy.float64` types are allowed. Returns: cupy.ndarray: Samples drawn from the standard cauchy distribution. .. seealso:: :func:`numpy.random.standard_cauchy` )rrstandard_cauchyr r r s rr\r\s#(  $ $ &B  d **rcN[R"5nURX5$)a>Standard exponential distribution. Returns an array of samples drawn from the standard exponential distribution. Its probability density function is defined as .. math:: f(x) = e^{-x}. Args: size (int or tuple of ints): The shape of the array. If ``None``, a zero-dimensional array is generated. dtype: Data type specifier. Only :class:`numpy.float32` and :class:`numpy.float64` types are allowed. Returns: cupy.ndarray: Samples drawn from the standard exponential distribution. .. seealso:: :func:`numpy.random.standard_exponential` )rrstandard_exponentialr]s rr_r_s#(  $ $ &B " "4 //rcP[R"5nURXU5$)aStandard gamma distribution. Returns an array of samples drawn from the standard gamma distribution. Its probability density function is defined as .. math:: f(x) = \frac{1}{\Gamma(k)}x^{k-1}e^{-x}. Args: shape (array): Parameter of the gamma distribution :math:`k`. size (int or tuple of ints): The shape of the array. If ``None``, a zero-dimensional array is generated. dtype: Data type specifier. Only :class:`numpy.float32` and :class:`numpy.float64` types are allowed. Returns: cupy.ndarray: Samples drawn from the standard gamma distribution. .. seealso:: :func:`numpy.random.standard_gamma` )rrstandard_gamma)r'r r r s rraras%,  $ $ &B  U% 00rcN[R"5nURX5$)aReturns an array of samples drawn from the standard normal distribution. This is a variant of :func:`cupy.random.randn`. Args: size (int or tuple of ints): The shape of the array. If ``None``, a zero-dimensional array is generated. dtype: Data type specifier. Returns: cupy.ndarray: Samples drawn from the standard normal distribution. .. seealso:: :func:`numpy.random.standard_normal` )rrstandard_normalr]s rrcrcs#  $ $ &B  d **rcP[R"5nURXU5$)aStandard Student's t distribution. Returns an array of samples drawn from the standard Student's t distribution. Its probability density function is defined as .. math:: f(x) = \frac{\Gamma(\frac{\nu+1}{2})} {\sqrt{\nu\pi}\Gamma(\frac{\nu}{2})} \left(1 + \frac{x^2}{\nu} \right)^{-(\frac{\nu+1}{2})}. Args: df (float or array_like of floats): Degree of freedom :math:`\nu`. size (int or tuple of ints): The shape of the array. If ``None``, a zero-dimensional array is generated. dtype: Data type specifier. Only :class:`numpy.float32` and :class:`numpy.float64` types are allowed. Returns: cupy.ndarray: Samples drawn from the standard Student's t distribution. .. seealso:: :func:`numpy.random.standard_t` )rr standard_trs rreres#0  $ $ &B ==5 ))rcR[R"5nURXX#U5$)aTriangular distribution. Returns an array of samples drawn from the triangular distribution. Its probability density function is defined as .. math:: f(x) = \begin{cases} \frac{2(x-l)}{(r-l)(m-l)} & \text{for } l \leq x \leq m, \\ \frac{2(r-x)}{(r-l)(r-m)} & \text{for } m \leq x \leq r, \\ 0 & \text{otherwise}. \end{cases} Args: left (float): Lower limit :math:`l`. mode (float): The value where the peak of the distribution occurs. :math:`m`. right (float): Higher Limit :math:`r`. size (int or tuple of ints): The shape of the array. If ``None``, a zero-dimensional array is generated. dtype: Data type specifier. Only :class:`numpy.float32` and :class:`numpy.float64` types are allowed. Returns: cupy.ndarray: Samples drawn from the triangular distribution. .. seealso:: :func:`numpy.random.triangular` )rr triangular)leftmoderightr r r s rrgrgs%:  $ $ &B ==U% 88rcL[R"5nURXX#S9$)aUReturns an array of uniformly-distributed samples over an interval. Samples are drawn from a uniform distribution over the half-open interval ``[low, high)``. The samples may contain the ``high`` limit due to floating-point rounding. Args: low (float): Lower end of the interval. high (float): Upper end of the interval. size (int or tuple of ints): The shape of the array. If ``None``, a zero-dimensional array is generated. dtype: Data type specifier. Returns: cupy.ndarray: Samples drawn from the uniform distribution. .. seealso:: :func:`numpy.random.uniform` r9)rruniform)lowhighr r r s rrlrl8s%(  $ $ &B ::cd: 88rcL[R"5nURXX#S9$)avon Mises distribution. Returns an array of samples drawn from the von Mises distribution. Its probability density function is defined as .. math:: f(x) = \frac{e^{\kappa \cos(x-\mu)}}{2\pi I_0(\kappa)}. Args: mu (float): Parameter of the von Mises distribution :math:`\mu`. kappa (float): Parameter of the von Mises distribution :math:`\kappa`. size (int or tuple of ints): The shape of the array. If ``None``, a zero-dimensional array is generated. dtype: Data type specifier. Only :class:`numpy.float32` and :class:`numpy.float64` types are allowed. Returns: cupy.ndarray: Samples drawn from the von Mises distribution. .. seealso:: :func:`numpy.random.vonmises` r9)rrvonmises)mukappar r r s rrprpPs%.  $ $ &B ;;rt; 99rcP[R"5nURXX#5$)aWald distribution. Returns an array of samples drawn from the Wald distribution. Its probability density function is defined as .. math:: f(x) = \sqrt{\frac{\lambda}{2\pi x^3}}\ e^{\frac{-\lambda(x-\mu)^2}{2\mu^2x}}. Args: mean (float): Parameter of the wald distribution :math:`\mu`. scale (float): Parameter of the wald distribution :math:`\lambda`. size (int or tuple of ints): The shape of the array. If ``None``, a zero-dimensional array is generated. dtype: Data type specifier. Only :class:`numpy.float32` and :class:`numpy.float64` types are allowed. Returns: cupy.ndarray: Samples drawn from the wald distribution. .. seealso:: :func:`numpy.random.wald` )rrwald)r;rr r r s rrtrtks#0  $ $ &B 774 ,,rcL[R"5nURXUS9$)aVweibull distribution. Returns an array of samples drawn from the weibull distribution. Its probability density function is defined as .. math:: f(x) = ax^{(a-1)}e^{-x^a}. Args: a (float): Parameter of the weibull distribution :math:`a`. size (int or tuple of ints): The shape of the array. If ``None``, a zero-dimensional array is generated. dtype: Data type specifier. Only :class:`numpy.float32` and :class:`numpy.float64` types are allowed. Returns: cupy.ndarray: Samples drawn from the weibull distribution. .. seealso:: :func:`numpy.random.weibull` r9)rrweibullrNs rrvrvs%,  $ $ &B ::a%: 00rcL[R"5nURXUS9$)a{Zipf distribution. Returns an array of samples drawn from the Zipf distribution. Its probability mass function is defined as .. math:: f(x) = \frac{x^{-a}}{ \zeta (a)}, where :math:`\zeta` is the Riemann Zeta function. Args: a (float): Parameter of the beta distribution :math:`a`. size (int or tuple of ints): The shape of the array. If ``None``, a zero-dimensional array is generated. dtype: Data type specifier. Only :class:`numpy.int32` and :class:`numpy.int64` types are allowed. Returns: cupy.ndarray: Samples drawn from the Zipf distribution. .. seealso:: :func:`numpy.random.zipf` r9)rrzipfrNs rrxrxs%0  $ $ &B 771u7 --r)Nl)r$Nry)* __future__r cupy.randomrcupyrfloatrintrrrrr!r&r)r,r0r5r7r:r>r@rErKrMrPrSrUrXrZr\r_rarcrergrlrprtrvrxrrrs"" &6C*65)4e,:!.6U+BU/4(4#D.B@>Cd%063T/6cE=034"&S>6)-(!*E7:t#D.,u%4)-EEB+/eG6(4e$4T+2U+0#%00 $514U+(E*8(,59B#D90":6 u-814S.r