class_docstr: Fast sampling by numerical inversion of the CDF for a large class of
  continuous distributions in `scipy.stats`.
  
  Parameters
  ----------
  dist : rv_frozen object
      Frozen distribution object from `scipy.stats`. The list of supported
      distributions can be found in the Notes section. The shape parameters,
      `loc` and `scale` used to create the distributions must be scalars.
      For example, for the Gamma distribution with shape parameter `p`,
      `p` has to be a float, and for the beta distribution with shape
      parameters (a, b), both a and b have to be floats.
  domain : tuple of floats, optional
      If one wishes to sample from a truncated/conditional distribution,
      the domain has to be specified.
      The default is None. In that case, the random variates are not
      truncated, and the domain is inferred from the support of the
      distribution.
  ignore_shape_range : boolean, optional.
      If False, shape parameters that are outside of the valid range
      of values to ensure that the numerical accuracy (see Notes) is
      high, raise a ValueError. If True, any shape parameters that are valid
      for the distribution are accepted. This can be useful for testing.
      The default is False.
  random_state : {None, int, `numpy.random.Generator`,
                      `numpy.random.RandomState`}, optional
  
          A NumPy random number generator or seed for the underlying NumPy
          random number generator used to generate the stream of uniform
          random numbers.
          If `random_state` is None, it uses ``self.random_state``.
          If `random_state` is an int,
          ``np.random.default_rng(random_state)`` is used.
          If `random_state` is already a ``Generator`` or ``RandomState``
          instance then that instance is used.
  
  Attributes
  ----------
  loc : float
      The location parameter.
  random_state : {`numpy.random.Generator`, `numpy.random.RandomState`}
      The random state used in relevant methods like `rvs` (unless
      another `random_state` is passed as an argument to these methods).
  scale : float
      The scale parameter.
  
  Methods
  -------
  cdf
  evaluate_error
  ppf
  qrvs
  rvs
  support
  
  Notes
  -----
  The class creates an object for continuous distributions specified
  by `dist`. The method `rvs` uses a generator from
  `scipy.stats.sampling` that is created when the object is instantiated.
  In addition, the methods `qrvs` and `ppf` are added.
  `qrvs` generate samples based on quasi-random numbers from
  `scipy.stats.qmc`. `ppf` is the PPF based on the
  numerical inversion method in [1]_ (`NumericalInversePolynomial`) that is
  used to generate random variates.
  
  Supported distributions (`distname`) are:
  ``alpha``, ``anglit``, ``argus``, ``beta``, ``betaprime``, ``bradford``,
  ``burr``, ``burr12``, ``cauchy``, ``chi``, ``chi2``, ``cosine``,
  ``crystalball``, ``expon``, ``gamma``, ``gennorm``, ``geninvgauss``,
  ``gumbel_l``, ``gumbel_r``, ``hypsecant``, ``invgamma``, ``invgauss``,
  ``invweibull``, ``laplace``, ``logistic``, ``maxwell``, ``moyal``,
  ``norm``, ``pareto``, ``powerlaw``, ``t``, ``rayleigh``, ``semicircular``,
  ``wald``, ``weibull_max``, ``weibull_min``.
  
  `rvs` relies on the accuracy of the numerical inversion. If very extreme
  shape parameters are used, the numerical inversion might not work. However,
  for all implemented distributions, the admissible shape parameters have
  been tested, and an error will be raised if the user supplies values
  outside of the allowed range. The u-error should not exceed 1e-10 for all
  valid parameters. Note that warnings might be raised even if parameters
  are within the valid range when the object is instantiated.
  To check numerical accuracy, the method `evaluate_error` can be used.
  
  Note that all implemented distributions are also part of `scipy.stats`, and
  the object created by `FastGeneratorInversion` relies on methods like
  `ppf`, `cdf` and `pdf` from `rv_frozen`. The main benefit of using this
  class can be summarized as follows: Once the generator to sample random
  variates is created in the setup step, sampling and evaluation of
  the PPF using `ppf` are very fast,
  and performance is essentially independent of the distribution. Therefore,
  a substantial speed-up can be achieved for many distributions if large
  numbers of random variates are required. It is important to know that this
  fast sampling is achieved by inversion of the CDF. Thus, one uniform
  random variate is transformed into a non-uniform variate, which is an
  advantage for several simulation methods, e.g., when
  the variance reduction methods of common random variates or
  antithetic variates are be used ([2]_).
  
  In addition, inversion makes it possible to
  - to use a QMC generator from `scipy.stats.qmc` (method `qrvs`),
  - to generate random variates truncated to an interval. For example, if
  one aims to sample standard normal random variates from
  the interval (2, 4), this can be easily achieved by using the parameter
  `domain`.
  
  The location and scale that are initially defined by `dist`
  can be reset without having to rerun the setup
  step to create the generator that is used for sampling. The relation
  of the distribution `Y` with `loc` and `scale` to the standard
  distribution `X` (i.e., ``loc=0`` and ``scale=1``) is given by
  ``Y = loc + scale * X``.
  
  References
  ----------
  .. [1] Derflinger, Gerhard, Wolfgang Hörmann, and Josef Leydold.
         "Random variate  generation by numerical inversion when only the
         density is known." ACM Transactions on Modeling and Computer
         Simulation (TOMACS) 20.4 (2010): 1-25.
  .. [2] Hörmann, Wolfgang, Josef Leydold and Gerhard Derflinger.
         "Automatic nonuniform random number generation."
         Springer, 2004.
  
  Examples
  --------
  >>> import numpy as np
  >>> from scipy import stats
  >>> from scipy.stats.sampling import FastGeneratorInversion
  
  Let's start with a simple example to illustrate the main features:
  
  >>> gamma_frozen = stats.gamma(1.5)
  >>> gamma_dist = FastGeneratorInversion(gamma_frozen)
  >>> r = gamma_dist.rvs(size=1000)
  
  The mean should be approximately equal to the shape parameter 1.5:
  
  >>> r.mean()
  1.52423591130436  # may vary
  
  Similarly, we can draw a sample based on quasi-random numbers:
  
  >>> r = gamma_dist.qrvs(size=1000)
  >>> r.mean()
  1.4996639255942914  # may vary
  
  Compare the PPF against approximation `ppf`.
  
  >>> q = [0.001, 0.2, 0.5, 0.8, 0.999]
  >>> np.max(np.abs(gamma_frozen.ppf(q) - gamma_dist.ppf(q)))
  4.313394796895409e-08
  
  To confirm that the numerical inversion is accurate, we evaluate the
  approximation error (u-error), which should be below 1e-10 (for more
  details, refer to the documentation of `evaluate_error`):
  
  >>> gamma_dist.evaluate_error()
  (7.446320551265581e-11, nan)  # may vary
  
  Note that the location and scale can be changed without instantiating a
  new generator:
  
  >>> gamma_dist.loc = 2
  >>> gamma_dist.scale = 3
  >>> r = gamma_dist.rvs(size=1000)
  
  The mean should be approximately 2 + 3*1.5 = 6.5.
  
  >>> r.mean()
  6.399549295242894  # may vary
  
  Let us also illustrate how truncation can be applied:
  
  >>> trunc_norm = FastGeneratorInversion(stats.norm(), domain=(3, 4))
  >>> r = trunc_norm.rvs(size=1000)
  >>> 3 < r.min() < r.max() < 4
  True
  
  Check the mean:
  
  >>> r.mean()
  3.250433367078603  # may vary
  
  >>> stats.norm.expect(lb=3, ub=4, conditional=True)
  3.260454285589997
  
  In this particular, case, `scipy.stats.truncnorm` could also be used to
  generate truncated normal random variates.
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docstr: Support of the distribution.
  
  Returns
  -------
  a, b : float
      end-points of the distribution's support.
  
  Notes
  -----
  
  Note that the support of the distribution depends on `loc`,
  `scale` and `domain`.
  
  Examples
  --------
  
  >>> from scipy import stats
  >>> from scipy.stats.sampling import FastGeneratorInversion
  
  Define a truncated normal distribution:
  
  >>> d_norm = FastGeneratorInversion(stats.norm(), domain=(0, 1))
  >>> d_norm.support()
  (0, 1)
  
  Shift the distribution:
  
  >>> d_norm.loc = 2.5
  >>> d_norm.support()
  (2.5, 3.5)
code: def support(self):
      """Support of the distribution.
  
      Returns
      -------
      a, b : float
          end-points of the distribution's support.
  
      Notes
      -----
  
      Note that the support of the distribution depends on `loc`,
      `scale` and `domain`.
  
      Examples
      --------
  
      >>> from scipy import stats
      >>> from scipy.stats.sampling import FastGeneratorInversion
  
      Define a truncated normal distribution:
  
      >>> d_norm = FastGeneratorInversion(stats.norm(), domain=(0, 1))
      >>> d_norm.support()
      (0, 1)
  
      Shift the distribution:
  
      >>> d_norm.loc = 2.5
      >>> d_norm.support()
      (2.5, 3.5)
  
      """
      return self._domain_adj
  
imports: import math
  import numbers
  import numpy
  from scipy import stats
  from scipy import special
  from ._qmc import check_random_state, Halton, QMCEngine
  from ._unuran.unuran_wrapper import NumericalInversePolynomial
  from scipy._lib._util import check_random_state
label_desc: Use image node_id 14 for calling the FastGeneratorInversion obj's underlying member method code with example usage: obj.support() and returns: self