A study on the Selection Problems under Multiple criteriaamong Populations with Poisson distribution

• Main Authors: Yu-Ling Wu, 巫瑜羚
• Other Authors: Yao-Tsung Lai
• Format: Others
• Language: zh-TW
• Published: 2005
• Online Access: http://ndltd.ncl.edu.tw/handle/83736512543403354557

碩士 === 真理大學 === 數理科學研究所 === 93 ===      In this paper, we use an empirical Bayes approach to solve the selecting problem under Bayes framework. We focus on selecting the best population from k Poisson populations with some prior. Consider k(k≥2) populations π₁,...,π_k.Each population π_i has a Poisson distribution Poi(θ_i), whose parameters θ_i are unknown. <BR>     For given control values θ₀ and σ₀²,we are interested in selecting some population whose mean is the largest in the qualified subset in which each parameter is between σ₀² and θ₀.Therefore, in this paper, it involves one parameter and three criteria in the selecting problem. <BR>     An empirical Bayes rule would be proposed, and the asymptotical optimality of the proposed would be proved. Finally, some Monte Carlo simulation will be done to discover the behavior of the proposed rule and by the approach we get well result.