# Source code for mars.tensor.random.binomial

```#!/usr/bin/env python
# -*- coding: utf-8 -*-
# Copyright 1999-2021 Alibaba Group Holding Ltd.
#
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
#
# Unless required by applicable law or agreed to in writing, software
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and

import numpy as np

from ... import opcodes as OperandDef
from ...serialization.serializables import AnyField
from ..utils import gen_random_seeds
from .core import TensorRandomOperandMixin, handle_array, TensorDistribution

class TensorBinomial(TensorDistribution, TensorRandomOperandMixin):
_input_fields_ = ["n", "p"]
_op_type_ = OperandDef.RAND_BINOMIAL

_fields_ = "n", "p", "size"
n = AnyField("n")
p = AnyField("p")
_func_name = "binomial"

def __call__(self, n, p, chunk_size=None):
return self.new_tensor([n, p], None, raw_chunk_size=chunk_size)

[docs]def binomial(random_state, n, p, size=None, chunk_size=None, gpu=None, dtype=None):
r"""
Draw samples from a binomial distribution.

Samples are drawn from a binomial distribution with specified
parameters, n trials and p probability of success where
n an integer >= 0 and p is in the interval [0,1]. (n may be
input as a float, but it is truncated to an integer in use)

Parameters
----------
n : int or array_like of ints
Parameter of the distribution, >= 0. Floats are also accepted,
but they will be truncated to integers.
p : float or array_like of floats
Parameter of the distribution, >= 0 and <=1.
size : int or tuple of ints, optional
Output shape.  If the given shape is, e.g., ``(m, n, k)``, then
``m * n * k`` samples are drawn.  If size is ``None`` (default),
a single value is returned if ``n`` and ``p`` are both scalars.
Otherwise, ``mt.broadcast(n, p).size`` samples are drawn.
chunk_size : int or tuple of int or tuple of ints, optional
Desired chunk size on each dimension
gpu : bool, optional
Allocate the tensor on GPU if True, False as default
dtype : data-type, optional
Data-type of the returned tensor.

Returns
-------
out : Tensor or scalar
Drawn samples from the parameterized binomial distribution, where
each sample is equal to the number of successes over the n trials.

--------
scipy.stats.binom : probability density function, distribution or
cumulative density function, etc.

Notes
-----
The probability density for the binomial distribution is

.. math:: P(N) = \binom{n}{N}p^N(1-p)^{n-N},

where :math:`n` is the number of trials, :math:`p` is the probability
of success, and :math:`N` is the number of successes.

When estimating the standard error of a proportion in a population by
using a random sample, the normal distribution works well unless the
product p*n <=5, where p = population proportion estimate, and n =
number of samples, in which case the binomial distribution is used
instead. For example, a sample of 15 people shows 4 who are left
handed, and 11 who are right handed. Then p = 4/15 = 27%. 0.27*15 = 4,
so the binomial distribution should be used in this case.

References
----------
.. [1] Dalgaard, Peter, "Introductory Statistics with R",
Springer-Verlag, 2002.
.. [2] Glantz, Stanton A. "Primer of Biostatistics.", McGraw-Hill,
Fifth Edition, 2002.
.. [3] Lentner, Marvin, "Elementary Applied Statistics", Bogden
and Quigley, 1972.
.. [4] Weisstein, Eric W. "Binomial Distribution." From MathWorld--A
Wolfram Web Resource.
http://mathworld.wolfram.com/BinomialDistribution.html
.. [5] Wikipedia, "Binomial distribution",
http://en.wikipedia.org/wiki/Binomial_distribution

Examples
--------
Draw samples from the distribution:

>>> import mars.tensor as mt

>>> n, p = 10, .5  # number of trials, probability of each trial
>>> s = mt.random.binomial(n, p, 1000).execute()
# result of flipping a coin 10 times, tested 1000 times.

A real world example. A company drills 9 wild-cat oil exploration
wells, each with an estimated probability of success of 0.1. All nine
wells fail. What is the probability of that happening?

Let's do 20,000 trials of the model, and count the number that
generate zero positive results.

>>> (mt.sum(mt.random.binomial(9, 0.1, 20000) == 0)/20000.).execute()
# answer = 0.38885, or 38%.
"""
if dtype is None:
dtype = (
np.random.RandomState()
.binomial(handle_array(n), handle_array(p), size=(0,))
.dtype
)
size = random_state._handle_size(size)
seed = gen_random_seeds(1, random_state.to_numpy())[0]
op = TensorBinomial(seed=seed, size=size, gpu=gpu, dtype=dtype)
return op(n, p, chunk_size=chunk_size)
```