Non-stationary Markov chain with applications in the 2008 Australian open tennis tournament

• Main Authors: Sheng-ming Lee, 李勝明
• Other Authors: Jeng-fu Liu
• Format: Others
• Language: zh-TW
• Published: 2009
• Online Access: http://ndltd.ncl.edu.tw/handle/93535302532144211835

碩士 === 輔仁大學 === 應用統計學研究所 === 97 === In this study we consider that a special case of Markov chain is a stationary at each two-step and will stop at some time. After modifying our function, it will converge on the only absorbing state. Its transition probability matrix will be expanded by square matrix, andthe mean absorption time will be calculated by the fundamental matrix method. We use the example of the final four male singles in the 2008 Australian open tennis tournament. We estimate the service state distribution, return transition probability matrix, and mean return time. Finally, we can use those data to analyze player’s characteristic and to simulate tennis games.