numpy.random.RandomState.standard_t¶
method
-
RandomState.
standard_t
(df, size=None)¶ 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)
, thenm * n * k
samples are drawn. If size isNone
(default), a single value is returned ifdf
is a scalar. Otherwise,np.array(df).size
samples are drawn.
Returns: - out : ndarray or scalar
Drawn samples from the parameterized standard Student’s t distribution.
Notes
The probability density function for the t distribution is
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” https://en.wikipedia.org/wiki/Student’s_t-distribution Examples