We compute the tail asymptotics of the product of a beta random variable and a generalized gamma random variable which are independent and have general parameters. A special case of these asymptotics were proved and used in a recent work of Bubeck, Mossel, and R\u00e1cz in order to determine the tail asymptotics of the maximum degree of the preferential attachment tree. The proof presented here is simpler and highlights why these asymptotics hold.<\/p>\n","protected":false},"excerpt":{"rendered":"
We compute the tail asymptotics of the product of a beta random variable and a generalized gamma random variable which are independent and have general parameters. A special case of these asymptotics were proved and used in a recent work of Bubeck, Mossel, and R\u00e1cz in order to determine the tail asymptotics of the maximum […]<\/p>\n","protected":false},"featured_media":0,"template":"","meta":{"msr-url-field":"","msr-podcast-episode":"","msrModifiedDate":"","msrModifiedDateEnabled":false,"ep_exclude_from_search":false,"_classifai_error":"","msr-author-ordering":[{"type":"text","value":"Jim Pitman","user_id":0},{"type":"user_nicename","value":"miracz","user_id":32949}],"msr_publishername":"Institute of Mathematical Statistics","msr_publisher_other":"","msr_booktitle":"","msr_chapter":"","msr_edition":"","msr_editors":"","msr_how_published":"","msr_isbn":"","msr_issue":"","msr_journal":"Electronic Communications in 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