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題名 | 有限馬可夫鏈之和及l階馬可夫鏈之連續成功次數的漸近分佈=Asymptotic Distributions for the Sum of Finite Markov Chain and Success Runs in lth order Markov Chain |
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作者 | 蘇志成; | 書刊名 | 統計與資訊評論 |
卷期 | 16 2014.12[民103.12] |
頁次 | 頁19-32 |
分類號 | 319.14 |
關鍵詞 | Bernoulli隨機變數; 複合Poisson分佈; 幾何分佈; I階馬可夫鏈; Poisson逼近; 連續成功次數; Bernoulli random variable; Compound Poisson distribution; Geometric distribution; lth-order Markov chain; Poisson approximation; Success run.; |
語文 | 中文(Chinese) |
中文摘要 | 在本文中,我們探討有限馬可夫鏈之和及l階馬可夫鏈中之四種常見計算連續成功次數統計量的漸近分佈。首先,對一有限馬可夫鏈,我們建構一與原馬可夫鏈之和漸近等價的隨機變數,經由所建構的漸近等價隨機變數之極限分佈,我們可以得到一有限馬可夫鏈之和的複合Poisson逼近定理。其次,對一具有狀態空間為{0, 1}之l階馬可夫鏈,若我們將其視為一具有l維度狀態空間之馬可夫鏈,則我們可導出四種常見計算連續成功次數統計量的複合Poisson逼近定理。 |
英文摘要 | In this paper, we study the asymptotic distributions for the sum of finite Markov chain and four well-known statistics of counting the number of success runs in lth order Markov chain. First for a finite Markov chain, we construct a random variable which is asymptotically equivalent to the sum of the original Markov chain and whose limiting distribution is more easily derived. A compound Poisson approximation for the sum of finite Markov chain can be obtained. Secondly, if a lth order Markov chain with state space {0, 1} is regarded as a Markov chain with l-dimensional state space, then we can derive some compound Poisson approximations for the four well-known statistics of counting the number of success runs inlth order Markov chain. |
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