A simple approximation to the percentiles of the \(t\) distribution skewness and curtosis (Q1424622)

The author presents a new approximation to percentiles of the \(t\)-distribution based on the formula \(t_{\alpha, v}=z_{\alpha}+ (z_{\alpha}^3+z_{\alpha})/ [4v-1.2{1-\ln(\alpha)}]\), where \(z_{\alpha}\) denotes the upper \({\alpha}\) point of \(N(0,1)\) and \(v\) stands for degrees of freedom. This approximation is simple and accurate enough for most practical purposes and can be used in applied statistics courses where students do not have easy access to computer programs capable of generating critical \(t\) values for any \({\alpha}\) and any noninteger values of \(v\).