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>−</mo> <mn>1</mn> <mo>/</mo> <mn>2</mn> <...
Main Authors: | , , |
---|---|
Format: | Article |
Language: | English |
Published: |
MDPI AG
2019-11-01
|
Series: | Symmetry |
Subjects: | |
Online Access: | https://www.mdpi.com/2073-8994/11/11/1351 |
id |
doaj-5988f62c31404c3fa6f1c8c0f6e6d827 |
---|---|
record_format |
Article |
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>−</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>−</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 |
_version_ |
1724903505144053760 |