Premium
A SIMPLE IMPROVED‐ACCURACY NORMAL APPROXIMATION FOR x 2
Author(s) -
Lewis Toby
Publication year - 1988
Publication title -
australian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.434
H-Index - 41
eISSN - 1467-842X
pISSN - 0004-9581
DOI - 10.1111/j.1467-842x.1988.tb00472.x
Subject(s) - simple (philosophy) , mathematics , standard deviation , simplicity , order (exchange) , computer science , calculus (dental) , algorithm , statistics , physics , medicine , philosophy , dentistry , epistemology , finance , quantum mechanics , economics
summary The following approximation for χ 2 with v degrees of freedom is presented: 1/[1 ‐ 1/6 In(χ 2 / v )] is distributed approximately normally with mean 1 ‐ (9 v ) ‐1 and standard deviation (18v) ‐1/2 +(18v) ‐3/2 . For use without resort to computer capability it is shown to compare favourably with various existing approximations, on grounds either of simplicity or accuracy or both. There is little to be gained from modifying this simple formula in order to secure higher‐order agreement with the Cornish‐Fisher expansion. The formula is readily adapted to give a simple normal approximation for noncentral χ 2 .