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An extension of Lukacs's result
| Content Provider | Scilit |
|---|---|
| Author | Shanbhag, D. N. |
| Copyright Year | 1971 |
| Description | Consider X and Y to be independent and non-degenerate random variables. If X and Y are non-negative then it follows from (6) that for all given values z of X + Y, the expected values of X and $X^{2}$ are of the type λz and λ′ $z^{2}$, respectively, if and only if X and Y have the gamma distributions with the same scale parameter. This is an improvement over Lukacs's result (3). Since the characterization problems for the Poisson, binomial, negative binomial and normal distributions resemble the corresponding problem for the gamma distribution it is quite reasonable to expect the characterizations similar to the above for these distributions. This is established in what follows. |
| Related Links | https://www.cambridge.org/core/services/aop-cambridge-core/content/view/6560E14A352D0A67C70AE5524B61FC83/S0305004100046673a.pdf/div-class-title-an-extension-of-lukacs-s-result-div.pdf |
| Ending Page | 303 |
| Page Count | 3 |
| Starting Page | 301 |
| ISSN | 03050041 |
| e-ISSN | 14698064 |
| DOI | 10.1017/s0305004100046673 |
| Journal | Mathematical Proceedings of the Cambridge Philosophical Society |
| Issue Number | 2 |
| Volume Number | 69 |
| Language | English |
| Publisher | Cambridge University Press (CUP) |
| Publisher Date | 1971-03-01 |
| Access Restriction | Open |
| Subject Keyword | Mathematical Proceedings of the Cambridge Philosophical Society Particles and Fields Physics |
| Content Type | Text |
| Resource Type | Article |
| Subject | Mathematics |
