Source code for mars.tensor.random.noncentral_f

#!/usr/bin/env python
# -*- 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,
# 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 TensorNoncentralF(TensorDistribution, TensorRandomOperandMixin):
    _input_fields_ = ["dfnum", "dfden", "nonc"]
    _op_type_ = OperandDef.RAND_NONCENTRAL_F

    _fields_ = "dfnum", "dfden", "nonc", "size"
    dfnum = AnyField("dfnum")
    dfden = AnyField("dfden")
    nonc = AnyField("nonc")
    _func_name = "noncentral_f"

    def __call__(self, dfnum, dfden, nonc, chunk_size=None):
        return self.new_tensor([dfnum, dfden, nonc], None, raw_chunk_size=chunk_size)

[docs]def noncentral_f( random_state, dfnum, dfden, nonc, size=None, chunk_size=None, gpu=None, dtype=None ): """ Draw samples from the noncentral 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 > 1. `nonc` is the non-centrality parameter. Parameters ---------- dfnum : float or array_like of floats Numerator degrees of freedom, should be > 0. dfden : float or array_like of floats Denominator degrees of freedom, should be > 0. nonc : float or array_like of floats Non-centrality parameter, the sum of the squares of the numerator means, 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``, ``dfden``, and ``nonc`` are all scalars. Otherwise, ``np.broadcast(dfnum, dfden, nonc).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 noncentral Fisher distribution. Notes ----- When calculating the power of an experiment (power = probability of rejecting the null hypothesis when a specific alternative is true) the non-central F statistic becomes important. When the null hypothesis is true, the F statistic follows a central F distribution. When the null hypothesis is not true, then it follows a non-central F statistic. References ---------- .. [1] Weisstein, Eric W. "Noncentral F-Distribution." From MathWorld--A Wolfram Web Resource. .. [2] Wikipedia, "Noncentral F-distribution", Examples -------- In a study, testing for a specific alternative to the null hypothesis requires use of the Noncentral F distribution. We need to calculate the area in the tail of the distribution that exceeds the value of the F distribution for the null hypothesis. We'll plot the two probability distributions for comparison. >>> import mars.tensor as mt >>> import matplotlib.pyplot as plt >>> dfnum = 3 # between group deg of freedom >>> dfden = 20 # within groups degrees of freedom >>> nonc = 3.0 >>> nc_vals = mt.random.noncentral_f(dfnum, dfden, nonc, 1000000) >>> NF = np.histogram(nc_vals.execute(), bins=50, normed=True) # TODO(jisheng): implement mt.histogram >>> c_vals = mt.random.f(dfnum, dfden, 1000000) >>> F = np.histogram(c_vals.execute(), bins=50, normed=True) >>> plt.plot(F[1][1:], F[0]) >>> plt.plot(NF[1][1:], NF[0]) >>> """ if dtype is None: dtype = ( np.random.RandomState() .noncentral_f( handle_array(dfnum), handle_array(dfden), handle_array(nonc), size=(0,) ) .dtype ) size = random_state._handle_size(size) seed = gen_random_seeds(1, random_state.to_numpy())[0] op = TensorNoncentralF(size=size, seed=seed, gpu=gpu, dtype=dtype) return op(dfnum, dfden, nonc, chunk_size=chunk_size)