A SIMPLE IMPROVED‐ACCURACY NORMAL APPROXIMATION FOR x²

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 .