t 분포 퍼센트점의 직접근사공식

Direct approximations for t percentage points

본 연구에서는 t 분포 백분위점을 구하는 방법으로 표준정규분포의 백분위점을 이용하는 간접근사공식들과는 달리 p와 n만의 직접근사공식을 찾았다. Hoaglin이 $\chi^2$분포에 적용했던 탐색적분석과정을 거쳐서 찾아낸 이 공식은 그 형태가 간단하여 일상적인 자료분석에서 손쉽게 이용될 수 있을 뿐만 아니라 최대 상대오차가 1.2%밖에 되지않는 좋은 공식이다.

In contrast to the customary approximations based on standard normal percentage points, direct approximations involve simple functions of parameters (such as degrees of freedom and tail area of the t distributions). This article used techniques of exploratory data analysis following Hoaglin to develop direct approximations for percentage points in the commonly used portions of upper tail of the t distribution with small to moderate numbers of degrees of freedom. These approximations are convenient to use and they compare favorably in accuracy with the popular approximations based on standard normal percentage points such as Peiser's. They can be used as an initial value generator in algorithms for getting more accurate percentage points.