scipy: BUG: scipy.special.stdtri: calling with small `df` crashes kernel

Describe your issue.

For certain distributions in scipy.stats, for very low values of parameters, the kernel crashes.

With other distributions, such low values cause a warning or an exception, which is fine. But with some distributions it simply crashes. It should instead be handled correctly.

Note that all parameters being used are within the domain for that parameter, as shown in the code below.

I originally found this issue with the beta distribution. Before posting I wrote code which looked through all the other distributions to see if it could create a crash with them also. It only managed with the t distribution.

With all other distributions, funny values gives

• a warning like RuntimeWarning: overflow encountered in [divide/double_scalars/_ncf_ppf/_nct_ppf], RuntimeWarning: invalid value encountered in [multiply/divide/add/subtract/double_scalars], RuntimeWarning: divide by zero encountered in [divide/log], RuntimeWarning: floating point number truncated to an integer
• or an error like RuntimeError: Failed to converge after 100 iterations. (for scipy.stats.genexpon(5e-324, 5e-324, 5e-324).ppf(.2) and scipy.stats.studentized_range(2, 5e-10).ppf(.2)).

Reproducing Code Example

import scipy.stats
print([shape_param.domain for shape_param in scipy.stats.t._shape_info()])
# [[5e-324, inf]]
print(scipy.stats.t(1e-10).ppf(.2))
# -1e+100
print(scipy.stats.t(1e-20).ppf(.2))
# 1e+100
print(scipy.stats.t(1e-30).ppf(.2))
# KERNEL CRASHES with message: `STOP  SMALL, X, BIG not monotone in INVR`


import scipy.stats
print([shape_param.domain for shape_param in scipy.stats.beta._shape_info()])
# [[5e-324, inf], [5e-324, inf]]
print(scipy.stats.beta(a=1e-308, b=5).ppf(.2))
# 0.0
print(scipy.stats.beta(a=1e-309, b=5).ppf(.2))
# OverflowError: Error in function boost::math::tgamma<d>(d): Overflow Error
# (raises error, but kernel doesn't crash)
print(scipy.stats.beta(a=1e-323, b=5).ppf(.2))
# KERNEL CRASHES with message: `Assertion failed: *p_derivative >= 0, file ..\..\scipy\_lib\boost/boost/math/special_functions/beta.hpp, line 739`

Error message

# after print(scipy.stats.t(1e-30).ppf(.2))
STOP  SMALL, X, BIG not monotone in INVR

# after print(scipy.stats.beta(a=1e-323, b=5).ppf(.2))
Assertion failed: *p_derivative >= 0, file ..\..\scipy\_lib\boost/boost/math/special_functions/beta.hpp, line 739

SciPy/NumPy/Python version and system information

1.10.1 1.23.1 sys.version_info(major=3, minor=9, micro=4, releaselevel='final', serial=0)
Build Dependencies:
  blas:
    detection method: pkgconfig
    found: true
    include directory: c:/opt/openblas/if_32/64/include
    lib directory: c:/opt/openblas/if_32/64/lib
    name: openblas
    openblas configuration: USE_64BITINT= DYNAMIC_ARCH=1 DYNAMIC_OLDER= NO_CBLAS=
      NO_LAPACK= NO_LAPACKE= NO_AFFINITY=1 USE_OPENMP= PRESCOTT MAX_THREADS=4
    pc file directory: c:/opt/openblas/if_32/64/lib/pkgconfig
    version: 0.3.18
  lapack:
    detection method: pkgconfig
    found: true
    include directory: c:/opt/openblas/if_32/64/include
    lib directory: c:/opt/openblas/if_32/64/lib
    name: openblas
    openblas configuration: USE_64BITINT= DYNAMIC_ARCH=1 DYNAMIC_OLDER= NO_CBLAS=
      NO_LAPACK= NO_LAPACKE= NO_AFFINITY=1 USE_OPENMP= PRESCOTT MAX_THREADS=4
    pc file directory: c:/opt/openblas/if_32/64/lib/pkgconfig
    version: 0.3.18
Compilers:
  c:
    commands: cc
    linker: ld.bfd
    name: gcc
    version: 10.3.0
  c++:
    commands: c++
    linker: ld.bfd
    name: gcc
    version: 10.3.0
  cython:
    commands: cython
    linker: cython
    name: cython
    version: 0.29.33
  fortran:
    commands: gfortran
    linker: ld.bfd
    name: gcc
    version: 10.3.0
  pythran:
    include directory: C:\Users\runneradmin\AppData\Local\Temp\pip-build-env-u63ta2f1\overlay\Lib\site-packages\pythran
    version: 0.12.1
Machine Information:
  build:
    cpu: x86_64
    endian: little
    family: x86_64
    system: windows
  cross-compiled: false
  host:
    cpu: x86_64
    endian: little
    family: x86_64
    system: windows
Python Information:
  path: C:\Users\runneradmin\AppData\Local\Temp\cibw-run-a1px0t3e\cp39-win_amd64\build\venv\Scripts\python.exe
  version: '3.9'