Robust Brown-Forsythe and Robust Modified Brown-Forsythe ANOVA Tests Under Heteroscedasticity for Contaminated Weibull Distribution

ANOVAS robustos heterocedásticos Brown-Forsythe y Brown-Forsythe modificado para la distribución Weibull contaminada

In this study, robust Brown-Forsythe and robust Modified Brown-Forsythe ANOVA tests are proposed to take into consideration heteroscedastic and non-normality data sets with outliers. The non-normal data is assumed to be a two parameters Weibull distribution. Robust proposed tests are obtained by using robust mean and variance estimators based on median/ MAD and median/Qn methods instead of maximum likelihood. The behaviors of the robust proposed and classical ANOVA tests are examined by simulation study. The results shows that the proposed robust tests have good performance especially in the presence of heteroscedasticity and contamination.

En este estudio se proponen tests Brown-Forsythe y robustos Brown-Forsythe ANOVA para tener en cuenta la no-normalidad en datos debida a la presencia de datos atípicos. Se asume que los datos no-normales tienen una distribución Weibull de dos parámetros. Estos tests se construyen en base a estimadores robustos de media y varianza obtenidos con métodos basados en la mediana en vez de métodos de máxima verosimilitud. Se examina en comportamiento de estos tests con datos simulados. Los resultados muestran que éstos tienen un buen desempeño, especialmente en presencia de atípicos y datos contaminados.

Robust Brown-Forsythe and Robust Modified Brown-Forsythe ANOVA Tests Under Heteroscedasticity for Contaminated Weibull Distribution ANOVAS robustos heterocedásticos Brown-Forsythe y Brown-Forsythe modificado para la distribución Weibull contaminada DERYA KARAGÖ¹, TÜLAY SARAÇBASI²

¹Hacettepe University, Faculty of Science, Department of Statistics, Ankara, Turkey. PhD. Email: deryacal@hacettepe.edu.tr
²Hacettepe University, Faculty of Science, Department of Statistics, Ankara, Turkey. Professor. Email: toker@hacettepe.edu.tr

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Abstract

Key words: Brown-Forsythe, Modified Brown-Forsythe, ANOVA, Weibull Distribution.

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Resumen

Palabras clave: ANOVA, Brown-Forsythe, Brown-Forsythe modificado, distribución Weibull.

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Texto completo disponible en PDF

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References

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[Recibido en octubre de 2014. Aceptado en febrero de 2015]

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Este artículo se puede citar en LaTeX utilizando la siguiente referencia bibliográfica de BibTeX:

@ARTICLE{RCEv39n1a02,
    AUTHOR  = {Karagöz, Derya and Saraçbasi, Tülay,
    TITLE   = {{Robust Brown-Forsythe and Robust Modified Brown-Forsythe ANOVA Tests Under Heteroscedasticity for Contaminated Weibull Distribution}},
    JOURNAL = {Revista Colombiana de Estadística},
    YEAR    = {2016},
    volume  = {39},
    number  = {1},
    pages   = {17-32}
}

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