Computes the estimator of the tail index (alpha) using Hill (1975) or Nicolau & Rodrigues (2019) estimators and tests both the hypothesis that alpha is bigger or equal to 4, and that alpha is lower or equal to 2.
estimate.alpha(x, sig.lev = 0.05, tail.est = "Hill", k = 0.1)alpha: Value of the tail index (alpha) to be used in micss.
alpha.fit: Estimated tail index.
t4: Test of the null hypothesis alpha>=4 against alpha<4.
t2: Test of the null hypothesis alpha<=2 against alpha>2.
A numeric vector.
Significance level. The default value is 0.05.
Estimator of the tail index. The default value is "Hill", which uses Hill's (1975) estimator. "NR" uses Nicolau & Rodrigues (2019) estimator.
Fraction of the upper tail to be used to estimate of the tail index. The default value is 0.1.
Used internally by micss.
B. Hill (1975): A Simple General Approach to Inference About the Tail of a Distribution. The Annals of Mathematical Statistics 3, 1163-1174.
J. Nicolau and P.M.M. Rodrigues (2019): A new regression-based tail index estimator. The Review of Economics and Statistics 101, 667-680.