estimate.alpha: estimate.alpha

In micss: Modified Iterative Cumulative Sum of Squares Algorithm

estimate.alpha

Description

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.

Usage

estimate.alpha(x, sig.lev = 0.05, tail.est = "Hill", k = 0.1)

Arguments

x	A numeric vector.
sig.lev	Significance level. The default value is 0.05.
tail.est	Estimator of the tail index. The default value is "Hill", which uses Hill's (1975) estimator. "NR" uses Nicolau & Rodrigues (2019) estimator.
k	Fraction of the upper tail to be used to estimate of the tail index. The default value is 0.1.

Details

Used internally by micss.

Value

• 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.

References

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.

micss documentation built on Sept. 11, 2024, 6:46 p.m.