.. ****************************************************************************** .. * Copyright 2020-2021 Intel Corporation .. * .. * Licensed under the Apache License, Version 2.0 (the "License"); .. * you may not use this file except in compliance with the License. .. * You may obtain a copy of the License at .. * .. * http://www.apache.org/licenses/LICENSE-2.0 .. * .. * Unless required by applicable law or agreed to in writing, software .. * distributed under the License is distributed on an "AS IS" BASIS, .. * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. .. * See the License for the specific language governing permissions and .. * limitations under the License. .. *******************************************************************************/ Bernoulli Distribution ====================== Generates Bernoulli distributed random numbers. Details ******* Bernoulli random number generator fills the :math:n \times p numeric table with Bernoulli distributed values with the :math:p probability of success on a single trial, where :math:p \in R, :math:0 \leq p \leq 1. A variate is called Bernoulli distributed if after a trial it is equal to :math:1 with the probability of success :math:p and to :math:0 with the probability :math:1 - p. The probability distribution is given by: .. math:: p\{x = 1\} = p .. math:: p\{x = 0\} = 1 - p The cumulative distribution function is as follows: .. math:: F_p(x) = \begin{cases} 0, & x < 0 \\ 1 - p, & 0 \leq x < 1, x \in \mathbb{R} \\ 1, & x \geq 1 \end{cases} Batch Processing **************** .. rubric:: Algorithm Parameters Bernoulli distribution algorithm has the following parameters in addition to the common parameters specified in :ref:distributions: .. tabularcolumns:: |\Y{0.15}|\Y{0.15}|\Y{0.7}| .. list-table:: Algorithm Parameters for Bernoulli Distribution (Batch Processing) :header-rows: 1 :widths: 10 10 60 :align: left :class: longtable * - Parameter - Default Value - Description * - algorithmFPType - float - The floating-point type that the algorithm uses for intermediate computations. Can be float or double. * - method - defaultDense - Performance-oriented computation method, the only method supported by the algorithm. * - p - Not applicable - Success probability of a trial, required parameter. Examples ******** .. tabs:: .. tab:: Python* Batch Processing: - :daal4py_example:distributions_bernoulli_batch.py Performance Considerations ************************** To get the best overall performance when using the Bernoulli distribution random number generator, provide the 32-bit signed integer homogeneous numeric table constructed with enabled equal features. .. include:: ../../../opt-notice.rst