Bootstrap-based confidence intervals for the standard two-sided power distribution

Abstract

The two-parameter standard two-sided power family of distributions on (0, 1) is considered in this article. We propose bootstrap standard errors for the maximum likelihood estimators, as well as bootstrap confidence intervals for its parameters, once these important statistical measures of accuracy cannot be computed based on first-order asymptotic theory. We consider Monte Carlo simulation experiments to verify the performance of the bootstrap methods, and the numerical results are quite promising. Applications to real data are also considered to illustrate the proposed methodology in practice.

Keywords:

• Bootstrap
• Bootstrap standard error
• Maximum likelihood estimator
• Order statistics

2020 Mathematics Subject Classification:

• 62F10
• 62F40

Acknowledgment

The author is very grateful to the reviewer for the careful reading of the article and for valuable comments which led to a significant improvement in the manuscript. The author acknowledges the financial support of the Brazilian agency Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq: grant 303554/2022-3).

Disclosure statement

No potential conflict of interest was reported by the author.