Shape and change point analyses of the Birnbaum-Saunders-t hazard rate and associated estimation

Cecilia Azevedo; Víctor Leiva; Emilia Athayde; N. Balakrishnan

doi:10.1016/j.csda.2012.05.007

Shape and change point analyses of the Birnbaum-Saunders-t hazard rate and associated estimation

Cecilia Azevedo, Víctor Leiva, Emilia Athayde, N. Balakrishnan

Research output: Contribution to journal › Article › peer-review

49 Scopus citations

Abstract

The hazard rate is a statistical indicator commonly used in lifetime analysis. The Birnbaum-Saunders (BS) model is a life distribution originated from a problem pertaining to material fatigue that has been applied to diverse fields. The BS model relates the total time until failure to some type of cumulative damage that is normally distributed. The generalized BS (GBS) distribution is a class of positively skewed models with lighter and heavier tails than the BS distribution. Particular cases of GBS distributions are the BS and BS-Student-t (BS-t) models. In this paper, we discuss shape and change point analyses for the hazard rate of the BS-t distribution. In addition, we evaluate the performance of the maximum likelihood and moment estimators of this change point using Monte Carlo methods. We also present an application with a real life data set useful for survival analysis, which shows the convenience of knowing such instant of change for establishing a reduction in the dose and, as a consequence, in the cost of the treatment.

Original language	English
Pages (from-to)	3887-3897
Number of pages	11
Journal	Computational Statistics and Data Analysis
Volume	56
Issue number	12
DOIs	https://doi.org/10.1016/j.csda.2012.05.007
State	Published - Dec 2012
Externally published	Yes

Keywords

Failure rate
Generalized Birnbaum-Saunders distribution
Lifetime data
Likelihood methods
Moment estimation
Monte Carlo methods

Access to Document

10.1016/j.csda.2012.05.007

Cite this

@article{c829889baaf3412185a80cc9e57b3618,

title = "Shape and change point analyses of the Birnbaum-Saunders-t hazard rate and associated estimation",

abstract = "The hazard rate is a statistical indicator commonly used in lifetime analysis. The Birnbaum-Saunders (BS) model is a life distribution originated from a problem pertaining to material fatigue that has been applied to diverse fields. The BS model relates the total time until failure to some type of cumulative damage that is normally distributed. The generalized BS (GBS) distribution is a class of positively skewed models with lighter and heavier tails than the BS distribution. Particular cases of GBS distributions are the BS and BS-Student-t (BS-t) models. In this paper, we discuss shape and change point analyses for the hazard rate of the BS-t distribution. In addition, we evaluate the performance of the maximum likelihood and moment estimators of this change point using Monte Carlo methods. We also present an application with a real life data set useful for survival analysis, which shows the convenience of knowing such instant of change for establishing a reduction in the dose and, as a consequence, in the cost of the treatment.",

keywords = "Failure rate, Generalized Birnbaum-Saunders distribution, Lifetime data, Likelihood methods, Moment estimation, Monte Carlo methods",

author = "Cecilia Azevedo and V{\'i}ctor Leiva and Emilia Athayde and N. Balakrishnan",

note = "Funding Information: The authors wish to thank the Editor-in-Chief, Dr. Stanley Azen, the Associate Editor and two anonymous referees for their constructive comments on an earlier version of this manuscript. A part of this study was developed during a stay of two months of Dr. V{\'i}ctor Leiva in the Department of Mathematics and Applications and the Centre of Mathematics (CMat) of the Universidade do Minho in Braga, Portugal. This research was financed by FEDER Funds through “Programa Operacional Factores de Competitividade—COMPETE”, by Portuguese Funds through FCT—“Funda{\c c}{\~a}o para a Ci{\^e}ncia e a Tecnologia”, within the Project Est-C/MAT/UI0013/2011, by the CMat through the FCT Pluriannual Funding Program, Portugal, and by FONDECYT 1120879 grant, Chile.",

year = "2012",

month = dec,

doi = "10.1016/j.csda.2012.05.007",

language = "English",

volume = "56",

pages = "3887--3897",

journal = "Computational Statistics and Data Analysis",

issn = "0167-9473",

publisher = "Elsevier",

number = "12",

}

TY - JOUR

T1 - Shape and change point analyses of the Birnbaum-Saunders-t hazard rate and associated estimation

AU - Azevedo, Cecilia

AU - Leiva, Víctor

AU - Athayde, Emilia

AU - Balakrishnan, N.

N1 - Funding Information: The authors wish to thank the Editor-in-Chief, Dr. Stanley Azen, the Associate Editor and two anonymous referees for their constructive comments on an earlier version of this manuscript. A part of this study was developed during a stay of two months of Dr. Víctor Leiva in the Department of Mathematics and Applications and the Centre of Mathematics (CMat) of the Universidade do Minho in Braga, Portugal. This research was financed by FEDER Funds through “Programa Operacional Factores de Competitividade—COMPETE”, by Portuguese Funds through FCT—“Fundação para a Ciência e a Tecnologia”, within the Project Est-C/MAT/UI0013/2011, by the CMat through the FCT Pluriannual Funding Program, Portugal, and by FONDECYT 1120879 grant, Chile.

PY - 2012/12

Y1 - 2012/12

N2 - The hazard rate is a statistical indicator commonly used in lifetime analysis. The Birnbaum-Saunders (BS) model is a life distribution originated from a problem pertaining to material fatigue that has been applied to diverse fields. The BS model relates the total time until failure to some type of cumulative damage that is normally distributed. The generalized BS (GBS) distribution is a class of positively skewed models with lighter and heavier tails than the BS distribution. Particular cases of GBS distributions are the BS and BS-Student-t (BS-t) models. In this paper, we discuss shape and change point analyses for the hazard rate of the BS-t distribution. In addition, we evaluate the performance of the maximum likelihood and moment estimators of this change point using Monte Carlo methods. We also present an application with a real life data set useful for survival analysis, which shows the convenience of knowing such instant of change for establishing a reduction in the dose and, as a consequence, in the cost of the treatment.

AB - The hazard rate is a statistical indicator commonly used in lifetime analysis. The Birnbaum-Saunders (BS) model is a life distribution originated from a problem pertaining to material fatigue that has been applied to diverse fields. The BS model relates the total time until failure to some type of cumulative damage that is normally distributed. The generalized BS (GBS) distribution is a class of positively skewed models with lighter and heavier tails than the BS distribution. Particular cases of GBS distributions are the BS and BS-Student-t (BS-t) models. In this paper, we discuss shape and change point analyses for the hazard rate of the BS-t distribution. In addition, we evaluate the performance of the maximum likelihood and moment estimators of this change point using Monte Carlo methods. We also present an application with a real life data set useful for survival analysis, which shows the convenience of knowing such instant of change for establishing a reduction in the dose and, as a consequence, in the cost of the treatment.

KW - Failure rate

KW - Generalized Birnbaum-Saunders distribution

KW - Lifetime data

KW - Likelihood methods

KW - Moment estimation

KW - Monte Carlo methods

UR - http://www.scopus.com/inward/record.url?scp=84864127485&partnerID=8YFLogxK

U2 - 10.1016/j.csda.2012.05.007

DO - 10.1016/j.csda.2012.05.007

M3 - Article

AN - SCOPUS:84864127485

SN - 0167-9473

VL - 56

SP - 3887

EP - 3897

JO - Computational Statistics and Data Analysis

JF - Computational Statistics and Data Analysis

IS - 12

ER -

Shape and change point analyses of the Birnbaum-Saunders-t hazard rate and associated estimation

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this