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Open AccessArticle

Bias Reduction for the Marshall-Olkin Extended Family of Distributions with Application to an Airplane’s Air Conditioning System and Precipitation Data

1
Department of Statistics, Institute of Exact Sciences, Federal University of Juiz de Fora, Juiz de Fora MG 36036-900, Brazil
2
Departamento de Matemáticas, Facultad de Ingeniería, Universidad de Atacama, Copiapó 1530000, Chile
3
Departamento de Ciencias Matemáticasy Físicas, Facultad de Ingeniería, Universidad Católica de Temuco, Temuco 4780000, Chile
*
Author to whom correspondence should be addressed.
Symmetry 2020, 12(5), 851; https://doi.org/10.3390/sym12050851
Received: 13 April 2020 / Revised: 8 May 2020 / Accepted: 9 May 2020 / Published: 22 May 2020
The Marshall-Olkin extended family of distributions is an alternative for modeling lifetimes, and considers more or less asymmetry than its parent model, achieved by incorporating just one extra parameter. We investigate the bias of maximum likelihood estimators and use it to develop an estimator with less bias than traditional estimators, by a modification of the score function. Unlike other proposals, in this paper, we consider a bias reduction methodology that can be applied to any member of the family and not necessarily to any particular distribution. We conduct a Monte Carlo simulation in order to study the performance of the corrected estimators in finite samples. This simulation shows that the maximum likelihood estimator is quite biased and the proposed estimator is much less biased; in small sample sizes, the bias is reduced by around 50 percent. Two applications, related to the air conditioning system of an airplane and precipitations, are presented to illustrate the results. In those applications, the bias reduction for the shape parameters is close to 25% and the bias reduction also reduces, among others things, the width of the 95% confidence intervals for quantiles lower than 0.594. View Full-Text
Keywords: asymmetric distributions; bias correction; Marshall-Olkin extended family; maximum likelihood estimators asymmetric distributions; bias correction; Marshall-Olkin extended family; maximum likelihood estimators
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Magalhães, T.M.; Gómez, Y.M.; Gallardo, D.I.; Venegas, O. Bias Reduction for the Marshall-Olkin Extended Family of Distributions with Application to an Airplane’s Air Conditioning System and Precipitation Data. Symmetry 2020, 12, 851.

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