Skewness of Maximum Likelihood Estimators in the Weibull Censored Data

Skewness of Maximum Likelihood Estimators in the Weibull Censored Data

In this paper, we obtain a matrix formula of order <inline-formula> <math display="inline"> <semantics> <mrow> <msup> <mi>n</mi> <mrow> <mo>&#8722;</mo> <mn>1</mn> <mo>/</mo> <mn>2</mn> <...

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Main Authors: Tiago M. Magalhães, Diego I. Gallardo, Héctor W. Gómez
Format: Article
Language:English
Published: MDPI AG 2019-11-01
Series:Symmetry
Subjects:
maximum likelihood estimates
type i and ii censoring
skewness coefficient
weibull censored data
Online Access:https://www.mdpi.com/2073-8994/11/11/1351
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spelling doaj-5988f62c31404c3fa6f1c8c0f6e6d8272020-11-25T02:13:42ZengMDPI AGSymmetry2073-89942019-11-011111135110.3390/sym11111351sym11111351Skewness of Maximum Likelihood Estimators in the Weibull Censored DataTiago M. Magalhães0Diego I. Gallardo1Héctor W. Gómez2Department of Statistics, Institute of Exact Sciences, Federal University of Juiz de Fora, Juiz de Fora 36000-000, BrazilDepartamento de Matemática, Facultad de Ingeniería, Universidad de Atacama, Copiapó 1530000, ChileDepartamento de Matemáticas, Facultad de Ciencias Básicas, Universidad de Antofagasta, Antofagasta 1240000, ChileIn this paper, we obtain a matrix formula of order <inline-formula> <math display="inline"> <semantics> <mrow> <msup> <mi>n</mi> <mrow> <mo>&#8722;</mo> <mn>1</mn> <mo>/</mo> <mn>2</mn> </mrow> </msup> <mo>,</mo> </mrow> </semantics> </math> </inline-formula> where <i>n</i> is the sample size, for the skewness coefficient of the distribution of the maximum likelihood estimators in the Weibull censored data. The present result is a nice approach to verify if the assumption of the normality of the regression parameter distribution is satisfied. Also, the expression derived is simple, as one only has to define a few matrices. We conduct an extensive Monte Carlo study to illustrate the behavior of the skewness coefficient and we apply it in two real datasets.https://www.mdpi.com/2073-8994/11/11/1351maximum likelihood estimatestype i and ii censoringskewness coefficientweibull censored data
collection DOAJ
language English
format Article
sources DOAJ
author Tiago M. Magalhães
Diego I. Gallardo
Héctor W. Gómez
spellingShingle Tiago M. Magalhães
Diego I. Gallardo
Héctor W. Gómez
Skewness of Maximum Likelihood Estimators in the Weibull Censored Data
Symmetry
maximum likelihood estimates
type i and ii censoring
skewness coefficient
weibull censored data
author_facet Tiago M. Magalhães
Diego I. Gallardo
Héctor W. Gómez
author_sort Tiago M. Magalhães
title Skewness of Maximum Likelihood Estimators in the Weibull Censored Data
title_short Skewness of Maximum Likelihood Estimators in the Weibull Censored Data
title_full Skewness of Maximum Likelihood Estimators in the Weibull Censored Data
title_fullStr Skewness of Maximum Likelihood Estimators in the Weibull Censored Data
title_full_unstemmed Skewness of Maximum Likelihood Estimators in the Weibull Censored Data
title_sort skewness of maximum likelihood estimators in the weibull censored data
publisher MDPI AG
series Symmetry
issn 2073-8994
publishDate 2019-11-01
description In this paper, we obtain a matrix formula of order <inline-formula> <math display="inline"> <semantics> <mrow> <msup> <mi>n</mi> <mrow> <mo>&#8722;</mo> <mn>1</mn> <mo>/</mo> <mn>2</mn> </mrow> </msup> <mo>,</mo> </mrow> </semantics> </math> </inline-formula> where <i>n</i> is the sample size, for the skewness coefficient of the distribution of the maximum likelihood estimators in the Weibull censored data. The present result is a nice approach to verify if the assumption of the normality of the regression parameter distribution is satisfied. Also, the expression derived is simple, as one only has to define a few matrices. We conduct an extensive Monte Carlo study to illustrate the behavior of the skewness coefficient and we apply it in two real datasets.
topic maximum likelihood estimates
type i and ii censoring
skewness coefficient
weibull censored data
url https://www.mdpi.com/2073-8994/11/11/1351
work_keys_str_mv AT tiagommagalhaes skewnessofmaximumlikelihoodestimatorsintheweibullcensoreddata
AT diegoigallardo skewnessofmaximumlikelihoodestimatorsintheweibullcensoreddata
AT hectorwgomez skewnessofmaximumlikelihoodestimatorsintheweibullcensoreddata
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