Αi,#SSKJr SSKJr SSKJr SSKrSSKJr \(a SSKJ r SSK J r "SS \R5r g) ) annotations)Sequence) TYPE_CHECKINGN) distribution)Tensor) _DTypeLiteralc^\rSrSr%SrS\S'S\S'S\S'SU4SjjrSS jr\SS j5r \SS j5r /4SS jjr SS jr SSjr SSjrSSjrSSjrSrU=r$)Binomialao The Binomial distribution with size `total_count` and `probs` parameters. In probability theory and statistics, the binomial distribution is the most basic discrete probability distribution defined on :math:`[0, n] \cap \mathbb{N}`, which can be viewed as the number of times a potentially unfair coin is tossed to get heads, and the result of its random variable can be viewed as the sum of a series of independent Bernoulli experiments. The probability mass function (pmf) is .. math:: pmf(x; n, p) = \frac{n!}{x!(n-x)!}p^{x}(1-p)^{n-x} In the above equation: * :math:`total\_count = n`: is the size, meaning the total number of Bernoulli experiments. * :math:`probs = p`: is the probability of the event happening in one Bernoulli experiments. Args: total_count(int|Tensor): The size of Binomial distribution which should be greater than 0, meaning the number of independent bernoulli trials with probability parameter :math:`p`. The data type will be converted to 1-D Tensor with paddle global default dtype if the input :attr:`probs` is not Tensor, otherwise will be converted to the same as :attr:`probs`. probs(float|Tensor): The probability of Binomial distribution which should reside in [0, 1], meaning the probability of success for each individual bernoulli trial. If the input data type is float, it will be converted to a 1-D Tensor with paddle global default dtype. Examples: .. code-block:: python >>> import paddle >>> from paddle.distribution import Binomial >>> paddle.set_device('cpu') >>> paddle.seed(100) >>> rv = Binomial(100, paddle.to_tensor([0.3, 0.6, 0.9])) >>> print(rv.sample([2])) Tensor(shape=[2, 3], dtype=float32, place=Place(cpu), stop_gradient=True, [[31., 62., 93.], [29., 54., 91.]]) >>> print(rv.mean) Tensor(shape=[3], dtype=float32, place=Place(cpu), stop_gradient=True, [30.00000191, 60.00000381, 90. ]) >>> print(rv.entropy()) Tensor(shape=[3], dtype=float32, place=Place(cpu), stop_gradient=True, [2.94053698, 3.00781751, 2.51124287]) rdtyper total_countprobsc>[R"5UlURX5uUlUlURR n[TU]!U5 g)N) paddleget_default_dtyper _to_tensorr rshapesuper__init__)selfr r batch_shape __class__s \/var/www/html/banglarbhumi/venv/lib/python3.13/site-packages/paddle/distribution/binomial.pyrBinomial.__init__QsK--/ '+{'J$$*&&,,  %c^[U[5(a[R"X RS9nOURUl[U[ 5(a[R"XRS9nO[R "XRS9n[R"X/5$)zConvert the input parameters into Tensors if they were not and broadcast them Returns: list[Tensor]: converted total_count and probs. r ) isinstancefloatr to_tensorr intcastbroadcast_tensors)rr rs rrBinomial._to_tensorZsy eU # #$$U**=EDJ k3 ' ' **;jjIK ++kDK''(<==rc4URUR-$)zAMean of binomial distribution. Returns: Tensor: mean value. r rrs rmean Binomial.meanos$**,,rcTURUR-SUR- -$)zIVariance of binomial distribution. Returns: Tensor: variance value. r&r's rvarianceBinomial.variancexs&$**,DJJ??rc[U[5(d [S5e[R"S5 [ U5n[ UR 5n[ X-5n[R"URUS9n[R"URUS9n[R"[R"USS9U5n[R"X`R5sSSS5 $!,(df  g=f)a6Generate binomial samples of the specified shape. The final shape would be ``shape+batch_shape`` . Args: shape (Sequence[int], optional): Prepended shape of the generated samples. Returns: Tensor: Sampled data with shape `sample_shape` + `batch_shape`. The returned data type is the same as `probs`. z%sample shape must be Sequence object.F)rint32rN) rr TypeErrorrset_grad_enabledtupler broadcast_tor rbinomialr"r )rrr output_shape output_size output_probsamples rr8Binomial.samples%**CD D  $ $U +%LE 0 01K !45L --  K!--djj MK__ Kw7F;;vzz2, + +s B5C66 DcUR5nURU5n[R"U5U-R S5*$)a%Shannon entropy in nats. The entropy is .. math:: \mathcal{H}(X) = - \sum_{x \in \Omega} p(x) \log{p(x)} In the above equation: * :math:`\Omega`: is the support of the distribution. Returns: Tensor: Shannon entropy of binomial distribution. The data type is the same as `probs`. r)_enumerate_supportlog_probrexpsum)rvaluesr<s rentropyBinomial.entropysB ((*==(H%055a888rc[R"S[R"UR5-URS9nUR SS[ UR5--5nU$)zvReturn the support of binomial distribution [0, 1, ... ,n] Returns: Tensor: the support of binomial distribution r+r))r+)rarangemaxr r reshapelenr)rr?s rr;Binomial._enumerate_supportsY   4++, ,DJJ s43C3C/D(D DE rch[R"XRS9n[R"URS-5[R"URU- S-5- [R"US-5- n[R "UR R5Rn[R"UR USU- S9n[R"UU[R"U5--URU- [R"SU- 5--U*S9$)zLog probability density/mass function. Args: value (Tensor): The input tensor. Returns: Tensor: log probability. The data type is the same as `probs`. rg?r+)minrE)neginf) rr"r lgammar finforepsclip nan_to_numlog)rvaluelog_combrNrs rr<Binomial.log_probs E4 MM$**S0 1mmD,,u4s:; <mmECK( )  ll4::++,00 DJJCQW=  &**U++,##e+vzz!e)/DDE4   rcL[R"URU55$)zProbability density/mass function. Args: value (Tensor): The input tensor. Returns: Tensor: probability. The data type is the same as `probs`. )rr=r<)rrRs rprob Binomial.probszz$--.//rcUR5nURU5nURU5n[R"[R"U5[R "X455R S5$)aThe KL-divergence between two binomial distributions with the same :attr:`total_count`. The probability density function (pdf) is .. math:: KL\_divergence(n_1, p_1, n_2, p_2) = \sum_x p_1(x) \log{\frac{p_1(x)}{p_2(x)}} .. math:: p_1(x) = \frac{n_1!}{x!(n_1-x)!}p_1^{x}(1-p_1)^{n_1-x} .. math:: p_2(x) = \frac{n_2!}{x!(n_2-x)!}p_2^{x}(1-p_2)^{n_2-x} Args: other (Binomial): instance of ``Binomial``. Returns: Tensor: kl-divergence between two binomial distributions. The data type is the same as `probs`. r)r;r<rmultiplyr=subtractr>)rothersupport log_prob_1 log_prob_2s r kl_divergenceBinomial.kl_divergencesb0))+]]7+ ^^G, OO :&8  #a&  r)r rr )r int | Tensorrfloat | TensorreturnNone)r rarrbrcz list[Tensor])rcr)rz Sequence[int]rcr)rRrrcr)r[r rcr)__name__ __module__ __qualname____firstlineno____doc____annotations__rrpropertyr(r,r8r@r;r<rVr___static_attributes__ __classcell__)rs@rr r s.`  M&'&0>& &>'>0>> >*--@@-/329(  : 0  rr ) __future__rcollections.abcrtypingrrpaddle.distributionrrpaddle._typing.dtype_liker Distributionr rrrus3#$ ,7f|((fr