On the distribution of the leading statistics for the bounded deviated permutations

• Main Authors: Wei-Liang Chien, 簡維良
• Other Authors: Yen-chi Lin
• Format: Others
• Language: en_US
• Published: 2014
• Online Access: http://ndltd.ncl.edu.tw/handle/57511428741392299977

碩士 === 國立臺灣師範大學 === 數學系 === 102 === The purpose of the thesis is to investigate the distribution of the leading statistic in the bounded deviated permutations S_{n+1}^{ℓ,r}, assuming the uniform distribution in S_{n+1}^{ℓ,r}. Define the random variable X_{n} to take the value k if π₁=k+1 for π=π₁π₂⋯π_{n+1}∈S_{n+1}^{ℓ,r}. By considering the bivariate generating function A(z,u), we could calculate the expected value and the standard deviation for X_{n}. The method is then applied to three specific cases, S_{n+1}^{1,2}, S_{n+1}^{1,3} and S_{n+1}^{2,2}. Since the coefficients λ_{n,k} of the bivariate generating function do not have a closed form, we will apply the Hayman method to get its asymptotic formula. Finally, by running computer programs, the convergence of the normal distribution on these three cases are verified.