Empirical likelihood based confidence intervals for the tail index when γ<−1/2

Empirical mortality data reveals that there is a finite age limit in the life span of humans, which means that it has a negative tail index. So far, there is a little literature on the confidence intervals for the tail index, especially for the negative tail index. In this paper, we construct its empirical likelihood based confidence intervals when γ<−1/2, which is known as the irregular case and derive the asymptotic χ2(1) distribution. At last a limited simulation study is conducted, which indicates that our method is better than the normal approximation in the sense of coverage probability and less sensitive to the selection of k.