Draw samples from a standard Student’s t distribution with df degrees
A special case of the hyperbolic distribution. As df gets
large, the result resembles that of the standard normal
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.
(m, n, k)
m * n * k
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 – Drawn samples from the parameterized standard Student’s t distribution.
Tensor or scalar
The probability density function for the t distribution is
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.
Dalgaard, Peter, “Introductory Statistics With R”,
Wikipedia, “Student’s t-distribution”
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
>>> s = mt.random.standard_t(10, size=100000)
Calculate the t statistic, setting the ddof parameter to the unbiased
value so the divisor in the standard deviation will be degrees of
>>> 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
>>> (mt.sum(s<t) / float(len(s))).execute()
So the p-value is about 0.009, which says the null hypothesis has a
probability of about 99% of being true.