# 臺灣博碩士論文加值系統

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 在本論文,我們同時考慮高記錄值和低記錄值,即所謂的雙邊記錄值。我們給出雙邊記錄值個數的分佈和極限分佈。此外並探討雙邊記錄值發生時間的分佈及其相關的極限分佈,以及前後記錄時間差之尾端分佈。
 In this work, we consider both the upper record values and lower record values, the so-called two-sided record values. we study the exact and asymtotic distributions of the number of two-sided record values. Also we investigate the exact distribution and relative asymptotic distribution of the two-sided record times. Finally, we give the tail distribution of the two-sided inter-record times.
 Abstract................................................................................................... ii 1.Introduction............................................................................................1 2.Results for two-sided record values ..................................................... 3 2.1. Some results of the number of two-sided record values................ 4 2.2. Some results of the two-sided record times................................... 8 3.An example......................................................................................... 12 Appendix................................................................................................ 13 References............................................................................................... 20
 Chandler, K. N. (1952), The distribution and frequence of record values, J. R. Statist. Soc. Ser.B , 220-228.Chandler, K. N. (1952), The distribution and frequence of record values, J. R. Statist. Soc. Ser.B 14, 220-228.Foster, F. G. and Stuart, A. (1954), Distribution-free test in time-series based on the breaking of records, J. R. Statist. Soc. Ser.B 14, No.1, 1-22.Glick, N. (1978), Breking records and breaking boards, {\it Amer. math. Mon.} {\bf 85}, {\bf No}.1 , 2-26.Galambos, J. (1978), The asymptotic theory of extreme order statistics. John Wiley & Sons, New York.Shorrock, R. W. (1972a), A limit theorem for inter-record times, J. Appl. Prob. 9, 219-223.Shorrock, R. W. (1972b), On record values and record times, J. Appl. Prob. 9, 316-326.Shiryayev, A. N. (1996), {\it Probability}, Springer-Verlag, New York.Loe've, M. (1978), Probability throey, vol I. Springer-Verlag, New York.Weissman, I. (1995), Records from a power model of indepent observations, J. Appl. Prob. 32, 982-990.
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