Discussion about Tow Methods for Calculating the Estimation Interval

Based on the definitions of equal-probability symmetrical interval and equal-density symmetrical interval, tow methods for calculating the estimation inverval are proposed. Then through two methods, it is deduced that the equal-density symmetrical interval is the shortest estimation interval. And these methods are compared for F distribution and χ2 distribution respectively; in the same condition, the length of equal-density symmetrical interval is always shorter than that of equal-probability symmetrical interval, and the two estimation intervals are closer to each other along with the degree’s increasing.