Bondesson’s powers conjecture for generalized gamma convolutions
Let be a nonnegative generalized gamma convolution (GGC) random variable. Then, for every real , the random variable is also a GGC random variable. Equivalently, the class of GGC distributions is closed under taking powers of order at least one.
References
Primary source
Additional references
- Powers of generalized gamma convolutions — arXiv — Min Wang, Sheng Yin
Progress summary
Two 2026 preprints claim to prove Bondesson’s conjecture, but the newest authors call their argument only a candidate proof, so the problem is not yet settled.
Bondesson’s conjecture, posed in 2015, asserts that raising a generalized gamma convolution variable to any power preserves the generalized gamma convolution property.
2026 claimed proofs
A January 2026 preprint claims a proof for and related consequences. A September 2026 preprint by Min Wang and Sheng Yin presents a second approach through finite gamma convolutions, approximation, and weak closure, but explicitly labels it a candidate proof and requests feedback. No counterexample, retraction, referee report, or independent verification was found.
Current status (as of September 2026): The conjecture has two claimed proofs, with the newest explicitly unverified; no established resolution is recorded.
Solutions 0
No solutions have been posted yet.