caa a22 4500 477062903 CHVBK 20180405111406.0 cr unu---uuuuu 170330e19960901xx s 000 0 eng 10.1007/BF00050856 doi (NATIONALLICENCE)springer-10.1007/BF00050856 A characterization of certain discrete exponential families [Elektronische Daten] [T. Nguyen, A. Gupta, Y. Wang] For independent random variables X and Y, define % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D% aebbfv3ySLgzGueE0jxyaibaiGc9yrFr0xXdbba91rFfpec8Eeeu0x% Xdbba9frFj0-OqFfea0dXdd9vqaq-JfrVkFHe9pgea0dXdar-Jb9hs% 0dXdbPYxe9vr0-vr0-vqpWqaaeaabiGaciaacaqabeaadaqaaqGaaO% qaaiaabofaruWrL9MCNLwyaGqbciaa-bcacqGHHjIUcaWFGaGaa8hw% aiaa-TcacaWFzbaaaa!4551!\[{\rm{S}} \equiv X + Y\]. When the conditional expectations % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D% aebbfv3ySLgzGueE0jxyaibaiGc9yrFr0xXdbba91rFfpec8Eeeu0x% Xdbba9frFj0-OqFfea0dXdd9vqaq-JfrVkFHe9pgea0dXdar-Jb9hs% 0dXdbPYxe9vr0-vr0-vqpWqaaeaabiGaciaacaqabeaadaqaaqGaaO% qaaiaadweacaGGBbqefCuzVj3zPfgaiuGajaaqcaWFNbGccaGGOaGa% amiwaiaacMcacaGG8bGaam4uaiaac2facqGHHjIUcaWGHbGaaiikai% aadofacaGGPaaaaa!4BC4!\[E[g(X)|S] \equiv a(S)\]and % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D% aebbfv3ySLgzGueE0jxyaibaiGc9yrFr0xXdbba91rFfpec8Eeeu0x% Xdbba9frFj0-OqFfea0dXdd9vqaq-JfrVkFHe9pgea0dXdar-Jb9hs% 0dXdbPYxe9vr0-vr0-vqpWqaaeaabiGaciaacaqabeaadaqaaqGaaO% qaaiaadweacaGGBbGaamiAaiaacIcacaWGybGaaiykaiaacYhacaWG% tbGaaiyxaiabggMi6kaadkgacaGGOaGaam4uaiaacMcaaaa!4894!\[E[h(X)|S] \equiv b(S)\]are given, then under certain assumptions, the density function of X has the form of u(x)k(α)eax, where u(x) is uniquely determined by the functions a(·) and b(·). Kluwer Academic Publishers, 1996 Characterization nationallicence conditional expectation nationallicence Nguyen T. Department of Mathematics and Statistics, Bowling Green State University, 43403-0221, Bowling Green, OH, U.S.A. aut Gupta A. Department of Mathematics and Statistics, Bowling Green State University, 43403-0221, Bowling Green, OH, U.S.A. aut Wang Y. Department of Mathematics and Statistics, Bowling Green State University, 43403-0221, Bowling Green, OH, U.S.A. aut Annals of the Institute of Statistical Mathematics Kluwer Academic Publishers 48/3(1996-09-01), 573-576 0020-3157 48:3<573 1996 48 10463 https://doi.org/10.1007/BF00050856 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/BF00050856 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Nguyen T. Department of Mathematics and Statistics, Bowling Green State University, 43403-0221, Bowling Green, OH, U.S.A aut NATIONALLICENCE 700 1- Gupta A. Department of Mathematics and Statistics, Bowling Green State University, 43403-0221, Bowling Green, OH, U.S.A aut NATIONALLICENCE 700 1- Wang Y. Department of Mathematics and Statistics, Bowling Green State University, 43403-0221, Bowling Green, OH, U.S.A aut NATIONALLICENCE 773 0- Annals of the Institute of Statistical Mathematics Kluwer Academic Publishers 48/3(1996-09-01), 573-576 0020-3157 48:3<573 1996 48 10463 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer