A corrected normal approximation for the Student’s t distribution

✍ Scribed by Baibing Li; Bart De Moor

• Publisher: Elsevier Science
• Year: 1998
• Tongue: English
• Weight: 61 KB
• Volume: 29
• Category: Article
• ISSN: 0167-9473
• DOI: 10.1016/s0167-9473(98)00065-6

✦ Synopsis

For the Student's t cumulative distribution function F(x; n) with n ≥ 3 degrees of freedom, a corrected normal approximation, ( x), is proposed as an extension of the well-known ordinary normal approximation (x), where (x) is the standard normal cumulative distribution and = (x; n) is a shrinking factor (0¡ ¡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.