DIRECT EXMNSIONS FOR THE DISTRIBUTION FUNCTIONS AND DENSITY FUNCTIONS OF χ~2-TYPE AND t-TYPE DISTRIBUTED RANDOM VARIABLES

作     者：ZHENG ZUKANG(Department of Statistics & Operational Research, Fudan University, Shanghai 299433, China) ZHENG ZUKANG(Department of Statistics & Operational Research, Fudan University, Shanghai 299433, China)

作者机构：Department of Statistics and Operational Research Fudan University Shanghai 299433 China 

出 版 物：《Chinese Annals of Mathematics,Series B》 (数学年刊（B辑英文版）)

年 卷 期：1996年第17卷第3期

页      面：289-300页

核心收录：

学科分类：02[经济学] 0202[经济学-应用经济学] 020208[经济学-统计学] 07[理学] 0714[理学-统计学（可授理学、经济学学位）] 070103[理学-概率论与数理统计] 0701[理学-数学] 

主　　题：Edgeworth expansion Distribution function Density function 

摘      要：Suppose that Z1 , Z2,’’’ Zn are independent normal random variables with common meanμ and variance σ2. Then S2 and have distribution andtn-1 distribution respectively. If the normal assumption fails, there will be the remaindersof the distribution functions and density functions. This paper gives the direct expansions ofdistribution functions and density functions of S2 alld T up to o(n-1). They are more intuitiveand convenient than usual Edgeworth expansions.