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The discrete random variable is ``y = floor(x + offset)`` where x is the continuous random variable. Warning: not verified for all methods. add_scale : bool If True (default), then the scale of the base distribution is added as parameter for the discrete distribution. The scale parameter is in the last position. kwds : keyword arguments The extra keyword arguments are used delegated to the ``__init__`` of the super class. Their usage has not been checked, e.g. currently the support of the distribution is assumed to be all non-negative integers. Notes ----- `loc` argument is currently not supported, scale is not available for discrete distributions in scipy. The scale parameter of the underlying continuous distribution is the last shape parameter in this DiscretizedCount distribution if ``add_scale`` is True. The implementation was based mainly on [1]_ and [2]_. However, many new discrete distributions have been developed based on the approach that we use here. Note, that in many cases authors reparameterize the distribution, while this class inherits the parameterization from the underlying continuous distribution. References ---------- .. [1] Chakraborty, Subrata, and Dhrubajyoti Chakravarty. "Discrete gamma distributions: Properties and parameter estimations." Communications in Statistics-Theory and Methods 41, no. 18 (2012): 3301-3324. .. [2] Alzaatreh, Ayman, Carl Lee, and Felix Famoye. 2012. “On the Discrete Analogues of Continuous Distributions.” Statistical Methodology 9 (6): 589–603. c*tt| |Sr#)superr__new__)clsargskwds __class__s rrzDiscretizedCount.__new__"s[#.s33rc ||_||_|j|_||_|jat |jj d|_|rZ|jd|jdzi|xjdz c_n$|r|jddid|_nd|_t|(di|y)N,shapesz, srrnrr ) distrd_offset _ctor_param add_scalerlensplitk_shapesupdater__init__)rrrrrrs rrzDiscretizedCount.__init__'s    ,," << # 2 23 78DM Xu||e';<= "  XsO, ! !   4 rcBt|}|j|d<|S)Nr)r_updated_ctor_paramr)rdicrs rrz$DiscretizedCount._updated_ctor_param<s"g)+zzG  rcB|jr|d}|dd}||fSd}||fS)Nrr)r)rrscales r _unpack_argszDiscretizedCount._unpack_argsAs: >>HE9DU{EU{rN)rz random_statec |j|\}}| t|dd}tj|jj ||||d|j z}|S)N_sizer)rrzr)rgetattrrtruncrrvsr)rrzrrrrvs r_rvszDiscretizedCount._rvsIse''- e <4!,D XXndjjnnd%d2>@mm$% rc|j}|jdk7r||jz}|j|\}}|j|g|d|i|j|dzg|d|iz }|S)Nrrr)rrrsfrrrrrrs rr&zDiscretizedCount._pmfRsy  ==A DMM!A''- e UXXa ,$ ,e , UXXa!e 0d 0% 01rc|j}|j|\}}|jdk7r||jz}|j|dzg|d|i}|SNrrr)rrrrErs rrFzDiscretizedCount._cdf]s\ ''- e ==A DMM!A EIIa!e 0d 0% 0rc|j}|j|\}}|jdk7r||jz}|j|dzg|d|i}|Sr)rrrrrs r_sfzDiscretizedCount._sfes\ ''- e ==A DMM!A EHHQU /T / /rc|j}|j|\}}|j|g|d|i}|jdk7r||jz}t j |dz}|SNrrg?)rrrIrrfloorrrrrrqcrMs rrOzDiscretizedCount._ppfmk ''- e UYYq -4 -u - ==A dmm#B HHR9% &rc|j}|j|\}}|j|g|d|i}|jdk7r||jz}t j |dz}|Sr)rrisfrrrrs r_isfzDiscretizedCount._isfwrr)rT)r/r0r1r2rrrrrr&rFrrOr __classcell__rs@rrrsB,\4 !*  $$ rrc8eZdZdZdfd ZdZddZdZxZS)DiscretizedModelaexperimental model to fit discretized distribution Count models based on discretized distributions can be used to model data that is under- or over-dispersed relative to Poisson or that has heavier tails. Parameters ---------- endog : array_like, 1-D Univariate data for fitting the distribution. exog : None Explanatory variables are not supported. The ``exog`` argument is only included for consistency in the signature across models. distr : DiscretizedCount instance (required) Instance of a DiscretizedCount distribution. See Also -------- DiscretizedCount Examples -------- >>> from scipy import stats >>> from statsmodels.distributions.discrete import ( DiscretizedCount, DiscretizedModel) >>> dd = DiscretizedCount(stats.gamma) >>> mod = DiscretizedModel(y, distr=dd) >>> res = mod.fit() >>> probs = res.predict(which="probs", k_max=5) cb| tdt| ||||jj dt ||j z |_d|_|j |_ d|_ |j |_ dtj|jz|_y)Nexog is not supportedrrrg?) 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