Statistical Evidence in Experiments and in Record Values

Habibi, Amirali; Arghami, Nasser Reza; Ahmadi, Jafar

doi:10.1080/03610920600762780

Cited by 11 publications

(2 citation statements)

References 7 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Chandler's (1952) was firstly introduced theory and application of record values and formulated many of basic properties of them. Interested readers may refer to the works done by Glick (1978), Nagaraja (1988), Balakrishnan et al (1995), Arnold et al (1998), Habibi Rad et al (2006, Arashi and Emadi (2008), and Razmkhah and Ahmadi (2011). Now let X 1 = x 1 , .…”

Section: Introductionmentioning

confidence: 99%

On the Construction of Preliminary Test Estimator Based on Record Values for the Burr XII Model

Belaghi

Arashi

Tabatabaey

2014

Communications in Statistics - Theory and Methods

View full text Add to dashboard Cite

In this paper some different sorts of estimators are proposed based on record breaking observations in the Burr type XII model. We define Bayes as well as empirical Bayes preliminary test estimators in the same fashion as in the ordinary preliminary test estimator using relevant combinations of uniformly minimum variance unbiased (UMVU) and Bayes estimators. Exact and asymptotic bias and mean square error (MSE) expressions for the proposed estimators are derived under two different conditions of knowing the shape parameters. We compare the MSEs and obtain the confidence interval for the parameter of interest in which the preliminary test type estimators outperform the UMVU, Bayes and empirical Bayes estimators.An application of the ordinary preliminary test estimator is also considered. We conclude this approach by a useful discussion for practical purposes and a summary.

show abstract

Section: Introductionmentioning

confidence: 99%

On the Construction of Preliminary Test Estimator Based on Record Values for the Burr XII Model

Belaghi

Arashi

Tabatabaey

2014

Communications in Statistics - Theory and Methods

View full text Add to dashboard Cite

show abstract

“…Chandler (1952) introduced the concept of record values. Based on records, inferential procedures for the parameters of different distributions have been developed by Glick (1978), Nagaraja (1988a,b), Balakrishnan, Ahsanullah, and Chan (1995), Arnold, Balakrishnan, and Nagaraja (1992), Habibi, Arghami, and Ahmadi (2006), Arashi and Emadi (2008), Razmkhah, Morabbi, and Ahmadi (2012) and others.…”

Section: Introductionmentioning

confidence: 99%

Preliminary Test Estimators and Confidence Intervals for the Parametric Functions of the Moore and Bilikam Family of Lifetime Distributions Based on Records

Chaturvedi

Kang

Malhotra

2019

AJS

View full text Add to dashboard Cite

We consider two measures of reliability functions namely R(t)=P(X>t) and P=P(X>Y) for the Moore and Bilikam (1978) family of lifetime distributions which covers fourteen distributions as specific cases. For record data from this family of distributions, preliminary test estimators (PTEs) and preliminary test confidence interval (PTCI) based on uniformly minimum variance unbiased estimator (UMVUE), maximum likelihood estimator (MLE), empirical Bayes estimator (EBE) are obtained for the parameter. The bias and mean square error (MSE) (exact and asymptotic) of the proposed estimators are derived to study their relative efficiency and through simulation studies we establish that PTEs perform better than ordinary UMVUE, MLE and EBE. We also obtain the coverage probability (CP) and the expected length of the PTCI of the parameter and establish that the confidence intervals based on MLE are more precise. An application of the ordinary preliminary test estimator is also considered. To the best of the knowledge of the authors, no PTEs have been derived for R(t) and P based on records and thus we define improved PTEs based on MLE and UMVUE of R(t) and P. A comparative study of different methods of estimation done through simulations establishes that PTEs perform better than ordinary UMVUE and MLE.

show abstract

Estimation and Testing Procedures for the Reliability Functions of Exponentiated Generalized Family of Distributions and a Characterization Based on Records

Kumari

Pathak

2021

Springer Series in Reliability Engineering

View full text Add to dashboard Cite

Statistical Evidence in Experiments and in Record Values

Cited by 11 publications

References 7 publications

On the Construction of Preliminary Test Estimator Based on Record Values for the Burr XII Model

On the Construction of Preliminary Test Estimator Based on Record Values for the Burr XII Model

Preliminary Test Estimators and Confidence Intervals for the Parametric Functions of the Moore and Bilikam Family of Lifetime Distributions Based on Records

Estimation and Testing Procedures for the Reliability Functions of Exponentiated Generalized Family of Distributions and a Characterization Based on Records

Contact Info

Product

Resources

About