[doc] clarify the range of sampled rv for torch.tensor.exponential_ (#…

…113195)

Range of sampled random variable needs to be clarified for `torch.tensor.exponential_` whose supported interval is (0, inf) is different from [0, inf] of exponential distribution.

Background: #37984 (comment), #48841 (comment), #91673 (comment)

Pull Request resolved: #113195
Approved by: https://github.com/albanD

torch/_tensor_docs.py

@@ -1909,11 +1909,19 @@ def add_docstr_all(method, docstr):
     r"""
 exponential_(lambd=1, *, generator=None) -> Tensor
 
-Fills :attr:`self` tensor with elements drawn from the exponential distribution:
+Fills :attr:`self` tensor with elements drawn from the PDF (probability density function):
 
 .. math::
 
-    f(x) = \lambda e^{-\lambda x}
+    f(x) = \lambda e^{-\lambda x}, x > 0
+
+.. note::
+  In probability theory, exponential distribution is supported on interval [0, :math:`\inf`) (i.e., :math:`x >= 0`)
+  implying that zero can be sampled from the exponential distribution.
+  However, :func:`torch.Tensor.exponential_` does not sample zero,
+  which means that its actual support is the interval (0, :math:`\inf`).
+
+  Note that :func:`torch.distributions.exponential.Exponential` is supported on the interval [0, :math:`\inf`) and can sample zero.
 """,
 )