# -*- coding: utf-8 -*-
# Copyright 1999-2021 Alibaba Group Holding Ltd.
# 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
# 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.
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 TensorF(TensorDistribution, TensorRandomOperandMixin):
_input_fields_ = ['_dfnum', '_dfden']
_op_type_ = OperandDef.RAND_F
_fields_ = '_dfnum', '_dfden', '_size'
_dfnum = AnyField('dfnum')
_dfden = AnyField('dfden')
_func_name = 'f'
def __init__(self, size=None, dtype=None, **kw):
dtype = np.dtype(dtype) if dtype is not None else dtype
super().__init__(_size=size, dtype=dtype, **kw)
def __call__(self, dfnum, dfden, chunk_size=None):
return self.new_tensor([dfnum, dfden], None, raw_chunk_size=chunk_size)
[docs]def f(random_state, dfnum, dfden, size=None, chunk_size=None, gpu=None, dtype=None):
Draw samples from an F distribution.
Samples are drawn from an F distribution with specified parameters,
`dfnum` (degrees of freedom in numerator) and `dfden` (degrees of
freedom in denominator), where both parameters should be greater than
The random variate of the F distribution (also known as the
Fisher distribution) is a continuous probability distribution
that arises in ANOVA tests, and is the ratio of two chi-square
dfnum : float or array_like of floats
Degrees of freedom in numerator, should be > 0.
dfden : float or array_like of float
Degrees of freedom in denominator, should be > 0.
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 ``dfnum`` and ``dfden`` are both scalars.
Otherwise, ``np.broadcast(dfnum, dfden).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.
out : Tensor or scalar
Drawn samples from the parameterized Fisher distribution.
scipy.stats.f : probability density function, distribution or
cumulative density function, etc.
The F statistic is used to compare in-group variances to between-group
variances. Calculating the distribution depends on the sampling, and
so it is a function of the respective degrees of freedom in the
problem. The variable `dfnum` is the number of samples minus one, the
between-groups degrees of freedom, while `dfden` is the within-groups
degrees of freedom, the sum of the number of samples in each group
minus the number of groups.
..  Glantz, Stanton A. "Primer of Biostatistics.", McGraw-Hill,
Fifth Edition, 2002.
..  Wikipedia, "F-distribution",
An example from Glantz, pp 47-40:
Two groups, children of diabetics (25 people) and children from people
without diabetes (25 controls). Fasting blood glucose was measured,
case group had a mean value of 86.1, controls had a mean value of
82.2. Standard deviations were 2.09 and 2.49 respectively. Are these
data consistent with the null hypothesis that the parents diabetic
status does not affect their children's blood glucose levels?
Calculating the F statistic from the data gives a value of 36.01.
Draw samples from the distribution:
>>> import mars.tensor as mt
>>> dfnum = 1. # between group degrees of freedom
>>> dfden = 48. # within groups degrees of freedom
>>> s = mt.random.f(dfnum, dfden, 1000).execute()
The lower bound for the top 1% of the samples is :
So there is about a 1% chance that the F statistic will exceed 7.62,
the measured value is 36, so the null hypothesis is rejected at the 1%
if dtype is None:
dtype = np.random.RandomState().f(
handle_array(dfnum), handle_array(dfden), size=(0,)).dtype
size = random_state._handle_size(size)
seed = gen_random_seeds(1, random_state.to_numpy())
op = TensorF(seed=seed, size=size, gpu=gpu, dtype=dtype)
return op(dfnum, dfden, chunk_size=chunk_size)