Failures seen in unittest test_gluon_probability{_v1,_v2}.py::test_gluon_cauchy_{v1,}

[DickJC123]

Description

This was observed during the development of #18424. I've developed a fix which I've added via commit 29286c3. I observed that the failures occurred when the sample was near one or both ends of the unit normal distribution for the samples data input. Repro commands provided below.

Occurrences

MXNET_TEST_SEED=783333771 pytest --verbose -s tests/python/unittest/test_gluon_probability_v2.py::test_gluon_cauchy
MXNET_TEST_SEED=1447693795 pytest --verbose -s tests/python/unittest/test_gluon_probability_v2.py::test_gluon_cauchy
MXNET_TEST_SEED=952434416 pytest --verbose -s tests/python/unittest/test_gluon_probability_v1.py::test_gluon_cauchy_v1

[xidulu]

@DickJC123
It looks like your commits have solved this issue. Thanks for that.

This reason behind, is the heavy-tailed property of Cauchy, when the input for the quantile/icdf function is close to 1 or 0, the output will blow up, causing flaky tests.