Table 1.

 Bias ($\times {10}^3$; average of [estimate minus true α]) for tail-index estimators $B_1,B_2,B_3$, HI.N, HI.M, HI.Opt, and MHB3 with sample size $n={10}^4$ from $F(1,\alpha )$

α	B1	B2	B3	HI.N	HI.M	HI.Opt	MHB3
0.1	–5.24	–3.87	–3.00	10.25	135.16	–0.92	–5.82
0.2	– 11.96	– 6.88	– 3.79	– 9.31	73.52	– 1.73	– 9.65
0.3	–19.43	–8.55	–2.38	–25.60	30.89	–2.05	–12.03
0.4	– 27.72	– 9.75	0.63	– 32.82	4.87	– 1.54	– 13.44
0.5	–35.03	–8.91	5.96	–29.40	–5.30	1.42	–12.56
0.6	–43.76	–10.44	9.41	–24.21	–8.21	6.67	–10.26
0.7	–50.27	–11.28	12.19	–10.06	0.13	19.37	–3.26
0.8	–53.49	–12.55	11.48	31.58	37.82	51.80	7.30
0.9	–50.31	–13.69	5.46	204.26	208.27	153.44	5.45