Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
7547877 | Statistics & Probability Letters | 2018 | 6 Pages |
Abstract
The density function of t-distribution with n degrees of freedom is given by the following formula: fn(x)=Î(n+12)ÏnÎ(n2)1+x2nâ(n+1)â2,x>0.Ding (1988) obtained the following asymptotic formula in terms of 1ân: fn(x)=Ï(x){1+x4â2x2â14n+3x8â28x6+30x4+12x2+396n2+O1n3},nââ,which derives the known result limnââfn(x)=Ï(x), where Ï(x)=12Ïeâx2â2 is the probability density function of the standard normal distribution. In this paper, we develop Ding's result to produce a complete asymptotic expansion.
Related Topics
Physical Sciences and Engineering
Mathematics
Statistics and Probability
Authors
Chao-Ping Chen,