A corrected normal approximation for the Student's t distribution

被引：8

作者：

Li, BB ^{[1
]}

De Moor, B ^{[1
]}

机构：

[1] Katholieke Univ Leuven, Dept Elect Engn, ESAT, SISTA, B-3001 Heverlee, Belgium

来源：

COMPUTATIONAL STATISTICS & DATA ANALYSIS | 1998年 / 29卷 / 02期

关键词：

approximation; normal distribution; Student's t distribution;

D O I：

10.1016/S0167-9473(98)00065-6

中图分类号：

TP39 [计算机的应用];

学科分类号：

081203 ; 0835 ;

摘要：

For the Student's t cumulative distribution function F(x; n) with n greater than or equal to 3 degrees of freedom, a corrected normal approximation, Phi(lambda x), is proposed as an extension of the well-known ordinary normal approximation Phi(x), where Phi(x) is the standard normal cumulative distribution and lambda=lambda(x,n) is a shrinking factor (0<lambda<1). This approximation has a theoretical error O(1/n(2)) uniformly in x. Numerical results show that it can give satisfactory accuracy for even very small n. Thus, it provides a competitive alternative because of its reasonable balance between accuracy and simplicity. (C) 1999 Elsevier Science B.V. All rights reserved.

引用

页码：213 / 216

页数：4