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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. |
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系所名稱 Department |
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畢業學年期 Year, semester |
語文別 Language |
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學位類別 Degree |
頁數 Number of pages |
16 |
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研究生 Author |
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指導教授 Advisor |
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召集委員 Convenor |
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口試委員 Advisory Committee |
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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 |
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統計 Statistics |
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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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