2020-08-05T19:34:24Zhttps://repository.dl.itc.u-tokyo.ac.jp/?action=repository_oaipmhoai:repository.dl.itc.u-tokyo.ac.jp:000400312020-07-10T06:57:17Z00312:06865:06909:0691000009:00504:06868:06911:06912
Uniform Estimates for Distributions of the Sum of i.i.d. Random Variables with Fat Tail in the Threshold Caseenghttp://hdl.handle.net/2261/53534Departmental Bulletin PaperNakahara, KenjiWe show uniform estimates for distributions of the sum of i.i.d. random variables in the threshold case. Rozovskii showed several uniform estimates but the speed of convergence was not known. Our main uniform estimate implies a speed of convergence. We also compare our estimates with Nagaev's estimate which is valid in the non-threshold case and, moreover, give a necessary and sufficient condition for Nagaev's estimate to hold in the threshold case.Journal of mathematical sciences, the University of Tokyo1843974272012-03-3013405705AA11021653415https://repository.dl.itc.u-tokyo.ac.jp/?action=repository_action_common_download&item_id=40031&item_no=1&attribute_id=19&file_no=1Graduate School of Mathematical Sciences, The University of Tokyo2017-06-14