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博碩士論文 etd-0626102-204857 詳細資訊
Title page for etd-0626102-204857
論文名稱
Title
稀分更新過程之逆過程的探討
A Study of Inverses of Thinned Renewal Processes.
系所名稱
Department
畢業學年期
Year, semester
語文別
Language
學位類別
Degree
頁數
Number of pages
16
研究生
Author
指導教授
Advisor
召集委員
Convenor
口試委員
Advisory Committee
口試日期
Date of Exam
2002-06-01
繳交日期
Date of Submission
2002-06-26
關鍵字
Keywords
Gamma-c分佈、Markov鏈、Poisson 過程、負二項分佈、更新過程、稀分更新過程、Laplace 轉換、完全單調
Laplace transform, negative binomial distribution, renewal process, thinned point process, completely monotone, Poisson process, Markov chain, Gamma-c distribution
統計
Statistics
本論文已被瀏覽 5715 次,被下載 2502
The thesis/dissertation has been browsed 5715 times, has been downloaded 2502 times.
中文摘要
我們討論有關更新過程的稀分和Markov鏈稀分之性質,探討一些可由Markov鏈稀分得來之特殊的更新過程。
Abstract
We study the properties of thinning and Markov chain thinning of renewal processes. Among others, we investigate whether some special renewal processes can be obtained through Markov chain thinning.
目次 Table of Contents
1. Introduction
2. Preliminaries
3. Some basic properties for thinning via a Markov chain
4. Delayed gamma-c renewal processes
5. Delayed negative binomial renewal processes
6. An example
7. Discussion
參考文獻 References
1. Chandramohan, J. and Liang, L. K. (1985). Bernoulli, multinomial and markov chain thinning of some point processes and some results about the superposition of dependent renewal processes. J. Appl. Prob. 22, 828-835.
2. Chung, K. L. (1974). A Course in Probability Theory, 2nd ed., Academic Press, New York.
3. Feller, W. (1971). An Introduction to Probability Theory and Its Application, Vol 2, 2nd ed., John Wiley & Sons, New York.
4. Grandell, J. (1991). Aspects of Risk Theory. Springer-Verlag, New York.
5. Isham, V. (1980). Dependent thinning of point processes. J. Appl. Prob. 17, 987-995.
6. Kolsrud, T. (1986). Some comments on thinned renewal processes. Scand. Actuarial. J. , 236-241.
7. Yannaros, N. (1988). Some comments on the inverse problem for thinned renewal processes. Scand. Actuarial J. , 113-116.
8. Yannaros, N. (1988a). On Cox processes and gamma renewal processes. J. Appl. Prob. 25, 423-427.
9. Yannaros, N. (1988b). The inverses of thinned renewal processes. J. Appl. Prob. 25, 822-828.
10. Yannaros, N. (1991). Randomly observed random walks. Commun. tatist.-Stochastic Models. 7(2), 219-231.
11. Yannaros, N. (1994). Weibull renewal processes. Ann. Inst. Statist. Math. 46, 41-648.
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