Source code for mars.tensor.random.standard_t

#!/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,
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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 TensorStandardT(TensorDistribution, TensorRandomOperandMixin):
    _input_fields_ = ["df"]
    _op_type_ = OperandDef.RAND_STANDARD_T

    _fields_ = "df", "size"
    df = AnyField("df")
    _func_name = "standard_t"

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

[docs]def standard_t(random_state, df, size=None, chunk_size=None, gpu=None, dtype=None): r""" Draw samples from a standard Student's t distribution with `df` degrees of freedom. A special case of the hyperbolic distribution. As `df` gets large, the result resembles that of the standard normal distribution (`standard_normal`). Parameters ---------- df : float or array_like of floats Degrees of freedom, 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 ``df`` is a scalar. Otherwise, ``mt.array(df).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 standard Student's t distribution. Notes ----- The probability density function for the t distribution is .. math:: P(x, df) = \frac{\Gamma(\frac{df+1}{2})}{\sqrt{\pi df} \Gamma(\frac{df}{2})}\Bigl( 1+\frac{x^2}{df} \Bigr)^{-(df+1)/2} The t test is based on an assumption that the data come from a Normal distribution. The t test provides a way to test whether the sample mean (that is the mean calculated from the data) is a good estimate of the true mean. The derivation of the t-distribution was first published in 1908 by William Gosset while working for the Guinness Brewery in Dublin. Due to proprietary issues, he had to publish under a pseudonym, and so he used the name Student. References ---------- .. [1] Dalgaard, Peter, "Introductory Statistics With R", Springer, 2002. .. [2] Wikipedia, "Student's t-distribution"'s_t-distribution Examples -------- From Dalgaard page 83 [1]_, suppose the daily energy intake for 11 women in Kj is: >>> import mars.tensor as mt >>> intake = mt.array([5260., 5470, 5640, 6180, 6390, 6515, 6805, 7515, \ ... 7515, 8230, 8770]) Does their energy intake deviate systematically from the recommended value of 7725 kJ? We have 10 degrees of freedom, so is the sample mean within 95% of the recommended value? >>> s = mt.random.standard_t(10, size=100000) >>> mt.mean(intake).execute() 6753.636363636364 >>> intake.std(ddof=1).execute() 1142.1232221373727 Calculate the t statistic, setting the ddof parameter to the unbiased value so the divisor in the standard deviation will be degrees of freedom, N-1. >>> t = (mt.mean(intake)-7725)/(intake.std(ddof=1)/mt.sqrt(len(intake))) >>> import matplotlib.pyplot as plt >>> h = plt.hist(s.execute(), bins=100, normed=True) For a one-sided t-test, how far out in the distribution does the t statistic appear? >>> (mt.sum(s<t) / float(len(s))).execute() 0.0090699999999999999 #random So the p-value is about 0.009, which says the null hypothesis has a probability of about 99% of being true. """ if dtype is None: dtype = np.random.RandomState().standard_t(handle_array(df), size=(0,)).dtype size = random_state._handle_size(size) seed = gen_random_seeds(1, random_state.to_numpy())[0] op = TensorStandardT(size=size, seed=seed, gpu=gpu, dtype=dtype) return op(df, chunk_size=chunk_size)