pyuncertainnumber.pba.pbox_parametric
=====================================

.. py:module:: pyuncertainnumber.pba.pbox_parametric


Attributes
----------

.. autoapisummary::

   pyuncertainnumber.pba.pbox_parametric.normal
   pyuncertainnumber.pba.pbox_parametric.gaussian
   pyuncertainnumber.pba.pbox_parametric.named_pbox


Functions
---------

.. autoapisummary::

   pyuncertainnumber.pba.pbox_parametric.makePbox
   pyuncertainnumber.pba.pbox_parametric._bound_pcdf
   pyuncertainnumber.pba.pbox_parametric._parametric_bounds_array
   pyuncertainnumber.pba.pbox_parametric.norm
   pyuncertainnumber.pba.pbox_parametric.lognormal
   pyuncertainnumber.pba.pbox_parametric.alpha
   pyuncertainnumber.pba.pbox_parametric.anglit
   pyuncertainnumber.pba.pbox_parametric.argus
   pyuncertainnumber.pba.pbox_parametric.arcsine
   pyuncertainnumber.pba.pbox_parametric.beta
   pyuncertainnumber.pba.pbox_parametric.betaprime
   pyuncertainnumber.pba.pbox_parametric.bradford
   pyuncertainnumber.pba.pbox_parametric.burr
   pyuncertainnumber.pba.pbox_parametric.burr12
   pyuncertainnumber.pba.pbox_parametric.cauchy
   pyuncertainnumber.pba.pbox_parametric.chi
   pyuncertainnumber.pba.pbox_parametric.chi2
   pyuncertainnumber.pba.pbox_parametric.cosine
   pyuncertainnumber.pba.pbox_parametric.crystalball
   pyuncertainnumber.pba.pbox_parametric.dgamma
   pyuncertainnumber.pba.pbox_parametric.dweibull
   pyuncertainnumber.pba.pbox_parametric.erlang
   pyuncertainnumber.pba.pbox_parametric.exponnorm
   pyuncertainnumber.pba.pbox_parametric.exponential
   pyuncertainnumber.pba.pbox_parametric.exponweib
   pyuncertainnumber.pba.pbox_parametric.exponpow
   pyuncertainnumber.pba.pbox_parametric.f
   pyuncertainnumber.pba.pbox_parametric.fatiguelife
   pyuncertainnumber.pba.pbox_parametric.fisk
   pyuncertainnumber.pba.pbox_parametric.foldcauchy
   pyuncertainnumber.pba.pbox_parametric.foldnorm
   pyuncertainnumber.pba.pbox_parametric.genlogistic
   pyuncertainnumber.pba.pbox_parametric.gennorm
   pyuncertainnumber.pba.pbox_parametric.genpareto
   pyuncertainnumber.pba.pbox_parametric.genexpon
   pyuncertainnumber.pba.pbox_parametric.genextreme
   pyuncertainnumber.pba.pbox_parametric.gausshyper
   pyuncertainnumber.pba.pbox_parametric.gamma
   pyuncertainnumber.pba.pbox_parametric.gengamma
   pyuncertainnumber.pba.pbox_parametric.genhalflogistic
   pyuncertainnumber.pba.pbox_parametric.geninvgauss
   pyuncertainnumber.pba.pbox_parametric.gompertz
   pyuncertainnumber.pba.pbox_parametric.gumbel_r
   pyuncertainnumber.pba.pbox_parametric.gumbel_l
   pyuncertainnumber.pba.pbox_parametric.halfcauchy
   pyuncertainnumber.pba.pbox_parametric.halflogistic
   pyuncertainnumber.pba.pbox_parametric.halfnorm
   pyuncertainnumber.pba.pbox_parametric.halfgennorm
   pyuncertainnumber.pba.pbox_parametric.hypsecant
   pyuncertainnumber.pba.pbox_parametric.invgamma
   pyuncertainnumber.pba.pbox_parametric.invgauss
   pyuncertainnumber.pba.pbox_parametric.invweibull
   pyuncertainnumber.pba.pbox_parametric.irwinhall
   pyuncertainnumber.pba.pbox_parametric.jf_skew_t
   pyuncertainnumber.pba.pbox_parametric.johnsonsb
   pyuncertainnumber.pba.pbox_parametric.johnsonsu
   pyuncertainnumber.pba.pbox_parametric.kappa4
   pyuncertainnumber.pba.pbox_parametric.kappa3
   pyuncertainnumber.pba.pbox_parametric.ksone
   pyuncertainnumber.pba.pbox_parametric.kstwo
   pyuncertainnumber.pba.pbox_parametric.kstwobign
   pyuncertainnumber.pba.pbox_parametric.laplace
   pyuncertainnumber.pba.pbox_parametric.laplace_asymmetric
   pyuncertainnumber.pba.pbox_parametric.levy
   pyuncertainnumber.pba.pbox_parametric.levy_l
   pyuncertainnumber.pba.pbox_parametric.levy_stable
   pyuncertainnumber.pba.pbox_parametric.logistic
   pyuncertainnumber.pba.pbox_parametric.loggamma
   pyuncertainnumber.pba.pbox_parametric.loglaplace
   pyuncertainnumber.pba.pbox_parametric.loguniform
   pyuncertainnumber.pba.pbox_parametric.lomax
   pyuncertainnumber.pba.pbox_parametric.maxwell
   pyuncertainnumber.pba.pbox_parametric.mielke
   pyuncertainnumber.pba.pbox_parametric.moyal
   pyuncertainnumber.pba.pbox_parametric.nakagami
   pyuncertainnumber.pba.pbox_parametric.ncx2
   pyuncertainnumber.pba.pbox_parametric.ncf
   pyuncertainnumber.pba.pbox_parametric.nct
   pyuncertainnumber.pba.pbox_parametric.norminvgauss
   pyuncertainnumber.pba.pbox_parametric.pareto
   pyuncertainnumber.pba.pbox_parametric.pearson3
   pyuncertainnumber.pba.pbox_parametric.powerlaw
   pyuncertainnumber.pba.pbox_parametric.powerlognorm
   pyuncertainnumber.pba.pbox_parametric.powernorm
   pyuncertainnumber.pba.pbox_parametric.rdist
   pyuncertainnumber.pba.pbox_parametric.rayleigh
   pyuncertainnumber.pba.pbox_parametric.rel_breitwigner
   pyuncertainnumber.pba.pbox_parametric.rice
   pyuncertainnumber.pba.pbox_parametric.recipinvgauss
   pyuncertainnumber.pba.pbox_parametric.semicircular
   pyuncertainnumber.pba.pbox_parametric.skewcauchy
   pyuncertainnumber.pba.pbox_parametric.skewnorm
   pyuncertainnumber.pba.pbox_parametric.studentized_range
   pyuncertainnumber.pba.pbox_parametric.t
   pyuncertainnumber.pba.pbox_parametric.trapezoid
   pyuncertainnumber.pba.pbox_parametric.triang
   pyuncertainnumber.pba.pbox_parametric.truncweibull_min
   pyuncertainnumber.pba.pbox_parametric.tukeylambda
   pyuncertainnumber.pba.pbox_parametric.uniform_sps
   pyuncertainnumber.pba.pbox_parametric.vonmises
   pyuncertainnumber.pba.pbox_parametric.vonmises_line
   pyuncertainnumber.pba.pbox_parametric.wald
   pyuncertainnumber.pba.pbox_parametric.weibull_min
   pyuncertainnumber.pba.pbox_parametric.weibull_max
   pyuncertainnumber.pba.pbox_parametric.wrapcauchy
   pyuncertainnumber.pba.pbox_parametric.lognormal_weird
   pyuncertainnumber.pba.pbox_parametric.uniform
   pyuncertainnumber.pba.pbox_parametric.exponential_by_lambda
   pyuncertainnumber.pba.pbox_parametric.trapz
   pyuncertainnumber.pba.pbox_parametric.weibull
   pyuncertainnumber.pba.pbox_parametric.KM
   pyuncertainnumber.pba.pbox_parametric.KN
   pyuncertainnumber.pba.pbox_parametric.bernoulli
   pyuncertainnumber.pba.pbox_parametric.betabinom
   pyuncertainnumber.pba.pbox_parametric.betanbinom
   pyuncertainnumber.pba.pbox_parametric.binom
   pyuncertainnumber.pba.pbox_parametric.boltzmann
   pyuncertainnumber.pba.pbox_parametric.dlaplace
   pyuncertainnumber.pba.pbox_parametric.geom
   pyuncertainnumber.pba.pbox_parametric.hypergeom
   pyuncertainnumber.pba.pbox_parametric.logser
   pyuncertainnumber.pba.pbox_parametric.nbinom
   pyuncertainnumber.pba.pbox_parametric.nchypergeom_fisher
   pyuncertainnumber.pba.pbox_parametric.nchypergeom_wallenius
   pyuncertainnumber.pba.pbox_parametric.nhypergeom
   pyuncertainnumber.pba.pbox_parametric.planck
   pyuncertainnumber.pba.pbox_parametric.poisson
   pyuncertainnumber.pba.pbox_parametric.randint
   pyuncertainnumber.pba.pbox_parametric.skellam
   pyuncertainnumber.pba.pbox_parametric.yulesimon
   pyuncertainnumber.pba.pbox_parametric.zipf
   pyuncertainnumber.pba.pbox_parametric.zipfian


Module Contents
---------------

.. py:function:: makePbox(func) -> pyuncertainnumber.pba.pbox_abc.Pbox

.. py:function:: _bound_pcdf(dist_family, *args, **kwargs)

   bound the parametric CDF

   .. note::

      - top-level implemenatation
      - only support fully bounded parameters


.. py:function:: _parametric_bounds_array(dist_family, *args, **kwargs)

   from parametric distribution specification to define the lower and upper bound of the p-box

   :param dist_family: (str) the name of the distribution
   :param \*args: several parameter (interval or list)
   :param \*\*kwargs: scale parameters (interval or list)

   .. note:: - middle level implementation


.. py:function:: norm(*args)

.. py:function:: lognormal(*args)

.. py:function:: alpha(*args)

.. py:function:: anglit(*args)

.. py:function:: argus(*args)

.. py:function:: arcsine(*args)

.. py:function:: beta(*args)

.. py:function:: betaprime(*args)

.. py:function:: bradford(*args)

.. py:function:: burr(*args)

.. py:function:: burr12(*args)

.. py:function:: cauchy(*args)

.. py:function:: chi(*args)

.. py:function:: chi2(*args)

.. py:function:: cosine(*args)

.. py:function:: crystalball(*args)

.. py:function:: dgamma(*args)

.. py:function:: dweibull(*args)

.. py:function:: erlang(*args)

.. py:function:: exponnorm(*args)

.. py:function:: exponential(*args, **kwargs)

   The default p-box constructor for the exponential distribution with scale parameterisation

   .. note::

      scale parameterisation due to scipy.stats. Note that the "scale" argument is a must.
      There is an "exponential_by_lambda" constructor which uses the rate parameterisation.

   .. rubric:: Example

   >>> pba.pbox_parametric.exponential(scale=[1, 2])


.. py:function:: exponweib(*args)

.. py:function:: exponpow(*args)

.. py:function:: f(*args)

.. py:function:: fatiguelife(*args)

.. py:function:: fisk(*args)

.. py:function:: foldcauchy(*args)

.. py:function:: foldnorm(mu, s, steps=Params.steps)

.. py:function:: genlogistic(*args)

.. py:function:: gennorm(*args)

.. py:function:: genpareto(*args)

.. py:function:: genexpon(*args)

.. py:function:: genextreme(*args)

.. py:function:: gausshyper(*args)

.. py:function:: gamma(*args)

.. py:function:: gengamma(*args)

.. py:function:: genhalflogistic(*args)

.. py:function:: geninvgauss(*args)

.. py:function:: gompertz(*args)

.. py:function:: gumbel_r(*args)

.. py:function:: gumbel_l(*args)

.. py:function:: halfcauchy(*args)

.. py:function:: halflogistic(*args)

.. py:function:: halfnorm(*args)

.. py:function:: halfgennorm(*args)

.. py:function:: hypsecant(*args)

.. py:function:: invgamma(*args)

.. py:function:: invgauss(*args)

.. py:function:: invweibull(*args)

.. py:function:: irwinhall(*args)

.. py:function:: jf_skew_t(*args)

.. py:function:: johnsonsb(*args)

.. py:function:: johnsonsu(*args)

.. py:function:: kappa4(*args)

.. py:function:: kappa3(*args)

.. py:function:: ksone(*args)

.. py:function:: kstwo(*args)

.. py:function:: kstwobign(*args)

.. py:function:: laplace(*args)

.. py:function:: laplace_asymmetric(*args)

.. py:function:: levy(*args)

.. py:function:: levy_l(*args)

.. py:function:: levy_stable(*args)

.. py:function:: logistic(*args)

.. py:function:: loggamma(*args)

.. py:function:: loglaplace(*args)

.. py:function:: loguniform(*args)

.. py:function:: lomax(*args)

.. py:function:: maxwell(*args)

.. py:function:: mielke(*args)

.. py:function:: moyal(*args)

.. py:function:: nakagami(*args)

.. py:function:: ncx2(*args)

.. py:function:: ncf(*args)

.. py:function:: nct(*args)

.. py:function:: norminvgauss(*args)

.. py:function:: pareto(*args)

.. py:function:: pearson3(*args)

.. py:function:: powerlaw(*args)

.. py:function:: powerlognorm(*args)

.. py:function:: powernorm(*args)

.. py:function:: rdist(*args)

.. py:function:: rayleigh(*args, **kwargs)

.. py:function:: rel_breitwigner(*args)

.. py:function:: rice(*args)

.. py:function:: recipinvgauss(*args)

.. py:function:: semicircular(*args)

.. py:function:: skewcauchy(*args)

.. py:function:: skewnorm(*args)

.. py:function:: studentized_range(*args)

.. py:function:: t(*args)

.. py:function:: trapezoid(*args)

.. py:function:: triang(*args)

.. py:function:: truncweibull_min(*args)

.. py:function:: tukeylambda(*args)

.. py:function:: uniform_sps(*args)

.. py:function:: vonmises(*args)

.. py:function:: vonmises_line(*args)

.. py:function:: wald(*args)

.. py:function:: weibull_min(*args)

.. py:function:: weibull_max(*args)

.. py:function:: wrapcauchy(*args)

.. py:function:: lognormal_weird(mean, var, steps=Params.steps)

   p-box for the lognormal distribution

   *Note: the parameters used are the mean and variance of the lognormal distribution

   not the mean and variance of the underlying normal*
   See:
   `[1]<https://en.wikipedia.org/wiki/Log-normal_distribution#Generation_and_parameters>`
   `[2]<https://stackoverflow.com/questions/51906063/distribution-mean-and-standard-deviation-using-scipy-stats>`


   :param mean: mean of the lognormal distribution
   :param var: variance of the lognormal distribution

   :rtype: Pbox


.. py:function:: uniform(a, b, steps=Params.steps)

   special case of Uniform distribution as
   Scipy has an unbelivably strange parameterisation than common sense

   :param - a: (float) lower endpoint
   :param - b: (float) upper endpoints


.. py:function:: exponential_by_lambda(lamb: list | pyuncertainnumber.pba.intervals.number.Interval) -> pyuncertainnumber.pba.pbox_abc.Pbox

   Bespoke p-box constructor for the exponential distribution

   :param - lamb: (list or Interval) the rate parameter of the exponential distribution


.. py:function:: trapz(a, b, c, d, steps=Params.steps)

.. py:function:: weibull(*args, steps=Params.steps)

.. py:function:: KM(k, m, steps=Params.steps)

.. py:function:: KN(k, n, steps=Params.steps)

.. py:function:: bernoulli(*args)

.. py:function:: betabinom(*args)

.. py:function:: betanbinom(*args)

.. py:function:: binom(*args)

.. py:function:: boltzmann(*args)

.. py:function:: dlaplace(*args)

.. py:function:: geom(*args)

.. py:function:: hypergeom(*args)

.. py:function:: logser(*args)

.. py:function:: nbinom(*args)

.. py:function:: nchypergeom_fisher(*args)

.. py:function:: nchypergeom_wallenius(*args)

.. py:function:: nhypergeom(*args)

.. py:function:: planck(*args)

.. py:function:: poisson(*args)

.. py:function:: randint(*args)

.. py:function:: skellam(*args)

.. py:function:: yulesimon(*args)

.. py:function:: zipf(*args)

.. py:function:: zipfian(*args)

.. py:data:: normal

.. py:data:: gaussian

.. py:data:: named_pbox