Add the Student's t RandomVariable

aesara/tensor/random/basic.py

@@ -1370,6 +1370,60 @@ def rng_fn_scipy(cls, rng, b, loc, scale, size):
 truncexpon = TruncExponentialRV()
 
 
+class StudentTRV(ScipyRandomVariable):
+ r"""A Student's t continuous random variable.
+
+ The probability density function for `t` in terms of its degrees of freedom
+ parameter :math:`\nu`, location parameter :math:`\mu` and scale
+ parameter :math:`\sigma` is:
+
+ .. math::
+
+ f(x; \nu, \alpha, \beta) = \frac{\Gamma(\frac{\nu + 1}{2})}{\Gamma(\frac{\nu}{2})} \left(\frac{1}{\pi\nu\sigma}\right)^{\frac{1}{2}} \left[1+\frac{(x-\mu)^2}{\nu\sigma}\right]^{-\frac{\nu+1}{2}}
+
+ for :math:`\nu > 0`, :math:`\sigma > 0`.
+
+ """
+ name = "t"
+ ndim_supp = 0
+ ndims_params = [0, 0, 0]
+ dtype = "floatX"
+ _print_name = ("StudentT", "\\operatorname{StudentT}")
+
+ def __call__(self, df, loc=0.0, scale=1.0, size=None, **kwargs):
+ r"""Draw samples from a Student's t distribution.
+
+ Signature
+ ---------
+
+ `(), (), () -> ()`
+
+ Parameters
+ ----------
+ df
+ Degrees of freedom parameter :math:`\nu` of the distribution. Must be
+ positive.
+ loc
+ Location parameter :math:`\mu` of the distribution.
+ scale
+ Scale parameter :math:`\sigma` of the distribution. Must be
+ positive.
+ size
+ Sample shape. If the given size is `(m, n, k)`, then `m * n * k`
+ independent, identically distributed samples are returned. Default is
+ `None` in which case a single sample is returned.
+
+ """
+ return super().__call__(df, loc, scale, size=size, **kwargs)
+
+ @classmethod
+ def rng_fn_scipy(cls, rng, df, loc, scale, size):
+ return stats.t.rvs(df, loc=loc, scale=scale, size=size, random_state=rng)
+
+
+t = StudentTRV()
+
+
 class BernoulliRV(ScipyRandomVariable):
  r"""A Bernoulli discrete random variable.
 
@@ -2071,4 +2125,5 @@ def __call__(self, x, **kwargs):
  "standard_normal",
  "negative_binomial",
  "gengamma",
+ "t",
 ]

doc/library/tensor/random/basic.rst

@@ -145,6 +145,9 @@ Aesara can produce :class:`RandomVariable`\s that draw samples from many differe
 .. autoclass:: aesara.tensor.random.basic.StandardNormalRV
  :members: __call__
 
+.. autoclass:: aesara.tensor.random.basic.StudentTRV
+ :members: __call__
+
 .. autoclass:: aesara.tensor.random.basic.TriangularRV
  :members: __call__
 

tests/tensor/random/test_basic.py

@@ -48,6 +48,7 @@
  poisson,
  randint,
  standard_normal,
+ t,
  triangular,
  truncexpon,
  uniform,
@@ -926,6 +927,48 @@ def test_truncexpon_samples(b, loc, scale, size):
  )
 
 
+@pytest.mark.parametrize(
+ "df, loc, scale, size",
+ [
+ (
+ np.array(2, dtype=config.floatX),
+ np.array(0, dtype=config.floatX),
+ np.array(1, dtype=config.floatX),
+ None,
+ ),
+ (
+ np.array(2, dtype=config.floatX),
+ np.array(0, dtype=config.floatX),
+ np.array(1, dtype=config.floatX),
+ [],
+ ),
+ (
+ np.array(2, dtype=config.floatX),
+ np.array(0, dtype=config.floatX),
+ np.array(1, dtype=config.floatX),
+ [2, 3],
+ ),
+ (
+ np.full((1, 2), 5, dtype=config.floatX),
+ np.array(0, dtype=config.floatX),
+ np.array(1, dtype=config.floatX),
+ None,
+ ),
+ ],
+)
+def test_t_samples(df, loc, scale, size):
+ compare_sample_values(
+ t,
+ df,
+ loc,
+ scale,
+ size=size,
+ test_fn=lambda *args, size=None, random_state=None, **kwargs: t.rng_fn(
+ random_state, *(args + (size,))
+ ),
+ )
+
+
 @pytest.mark.parametrize(
  "p, size",
  [