Brazilian Journal of Probability and Statistics

The exponentiated logarithmic generated family of distributions and the evaluation of the confidence intervals by percentile bootstrap

Pedro Rafael Diniz Marinho, Gauss M. Cordeiro, Fernando Peña Ramírez, Morad Alizadeh, and Marcelo Bourguignon

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Abstract

We study some mathematical properties of a new generator of continuous distributions with three additional parameters, called the exponentiated logarithmic generated family, to extend the normal, Weibull, gamma and Gumbel distributions, among other well-known models. Some special models are discussed. Many properties of this family are studied, some inference procedures developed and a simulation study performed to verify the adequacy of the estimators of the model parameters. We prove empirically the potentiality of the new family by means of two real data sets. The simulation study for different samples sizes assesses the performance of the maximum likelihood estimates obtained by the Swarm Optimization method. We also evaluate the performance of single and dual bootstrap methods in constructing interval estimates for the parameters. Because of the intensive simulations, we use parallel computing on a supercomputer.

Article information

Source
Braz. J. Probab. Stat., Volume 32, Number 2 (2018), 281-308.

Dates
Received: May 2016
Accepted: November 2016
First available in Project Euclid: 17 April 2018

Permanent link to this document
https://projecteuclid.org/euclid.bjps/1523952016

Digital Object Identifier
doi:10.1214/16-BJPS343

Mathematical Reviews number (MathSciNet)
MR3787755

Zentralblatt MATH identifier
06914676

Keywords
Bootstrap generalized distribution lifetime logarithmic distribution mixture

Citation

Marinho, Pedro Rafael Diniz; Cordeiro, Gauss M.; Peña Ramírez, Fernando; Alizadeh, Morad; Bourguignon, Marcelo. The exponentiated logarithmic generated family of distributions and the evaluation of the confidence intervals by percentile bootstrap. Braz. J. Probab. Stat. 32 (2018), no. 2, 281--308. doi:10.1214/16-BJPS343. https://projecteuclid.org/euclid.bjps/1523952016


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