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Comparison of Bootstrap Confidence Intervals Using Monte Carlo Simulations

División Académica de Ingeniería y Arquitectura, Universidad Juárez Autónoma de Tabasco, Carretera Cunduacán—Jalpa de Méndez Km 1, Colonia la Esmeralda, Cunduacán 86080, Tabasco, Mexico
Unidad Académica de Ingeniería, Universidad Autónoma de Zacatecas, Av. Ramón López Velarde, 801, Zacatecas 98000, Mexico
Escuela Superior de Ingeniería y Arquitectura, Unidad Ticomán Ciencias de la Tierra, Instituto Politécnico Nacional, Avenida Ticomán 600, San José Ticomán, C.P. Delegación Gustavo A. Madero, Ciudad de México 07340, Mexico
Author to whom correspondence should be addressed.
Water 2018, 10(2), 166;
Received: 24 September 2017 / Revised: 11 January 2018 / Accepted: 29 January 2018 / Published: 8 February 2018
PDF [4463 KB, uploaded 8 February 2018]


Design of hydraulic works requires the estimation of design hydrological events by statistical inference from a probability distribution. Using Monte Carlo simulations, we compared coverage of confidence intervals constructed with four bootstrap techniques: percentile bootstrap (BP), bias-corrected bootstrap (BC), accelerated bias-corrected bootstrap (BCA) and a modified version of the standard bootstrap (MSB). Different simulation scenarios were analyzed. In some cases, the mother distribution function was fit to the random samples that were generated. In other cases, a distribution function different to the mother distribution was fit to the samples. When the fitted distribution had three parameters, and was the same as the mother distribution, the intervals constructed with the four techniques had acceptable coverage. However, the bootstrap techniques failed in several of the cases in which the fitted distribution had two parameters. View Full-Text
Keywords: Monte Carlo simulations; confidence intervals; coverage; bootstrap; maximum annual precipitation Monte Carlo simulations; confidence intervals; coverage; bootstrap; maximum annual precipitation

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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).

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Flowers-Cano, R.S.; Ortiz-Gómez, R.; León-Jiménez, J.E.; López Rivera, R.; Perera Cruz, L.A. Comparison of Bootstrap Confidence Intervals Using Monte Carlo Simulations. Water 2018, 10, 166.

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