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3402. Wording for negative_binomial_distribution is unclear as a consequence of LWG 2406 resolution

Section: [rand.dist.bern.negbin] Status: New Submitter: Ahti Leppänen Opened: 2020-02-17 Last modified: 2020-03-11

Priority: 3

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This issue has been created because a corresponding editorial change request had been rejected.

The resolution of LWG 2406 added a note to the definition of negative_binomial_distribution:

[Note: This implies that P(i|k,p) is undefined when p == 1. — end note]

This issue argues that the note is invalid as are the premises on which LWG 2406 was based on. It's also argued that current normative standard text allowing p == 1 is valid both conceptually and mathematically, and that it follows existing conventions in other software.

Problems with the added note:

Invalidity of premises of LWG 2406:

Validity of p == 1:

What comes to the reasons why p == 1 could have been considered invalid, it seems that major implementations — namely libstd++, libc++ and MSVC standard library — are using std::gamma_distribution in std::negative_binomial_distribution and passing (1 - p)/p as the second argument of std::gamma_distribution. Case p == 1 is not checked leading to violation of precondition of std::gamma_distribution, which requires argument to be > 0.

For these reasons the note added by resolution of LWG 2406 seems invalid and could be considered for removal. However given the current status and history regarding handling of case p == 1, removing the note might not be the only option to consider.

[2020-03-11 Issue Prioritization]

Priority to 3 and hand over to SG6 after reflector discussion.

Proposed resolution: