Preliminary test estimation of the parameters of exponential and Pareto distributions for censored samples

Kibria, B. M. Golam; Saleh, A. K. Md. Ehsanes

doi:10.1007/s00362-008-0163-y

Cited by 22 publications

(7 citation statements)

References 18 publications

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“…The readers are suggested to refer the articles cited in the bibliographies published earlier Bancroft and Han (1977) and Han et al (1988). Later on there were few more articles published on the preliminary test approaches and the latest among them are by Srivastava and Dulawat (2002) who obtained an estimator for average life of exponential population in presence of outliers using preliminary test and by Golam Kibria and Saleh (2008) who studied the estimation of the parameters of exponential and Pareto distribution for censored samples using a preliminary test.…”

Section: Classical and Preliminary Test-based Statistical Methodsmentioning

confidence: 96%

A review of preliminary test-based statistical methods for the benefit of Six Sigma quality practitioners

Ravichandran

2010

Stat Papers

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Ever since Professor Bancroft developed inference procedures using preliminary tests there has been a lot of research in this area by various authors across the world. This could be evidenced from two papers that widely reviewed the publications on preliminary test-based statistical methods. The use of preliminary tests in solving doubts arising over the model parameters has gained momentum as it has proven to be effective and powerful over to that of classical methods. Unfortunately, there has been a downward trend in research related to preliminary tests as it could be seen from only few recent publications. Obviously, the benefits of preliminary testbased statistical methods did not reach Six Sigma practitioners as the concept of Six Sigma just took off and it was in a premature state. In this paper, efforts have been made to present a review of the publications on the preliminary test-based statistical methods. Though studies on preliminary test-based methods have been done in various areas of statistics such as theory of estimation, hypothesis testing, analysis of variance, regression analysis, reliability, to mention a few, only few important methods are presented here for the benefit of readers, particularly Six Sigma quality practitioners, to understand the concept. In this regard, the define, measure, analyze, improve and control methodology of six sigma is presented with a link of analyze phase to preliminary test-based statistical methods. Examples are also given to illustrate the procedures.

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Section: Classical and Preliminary Test-based Statistical Methodsmentioning

confidence: 96%

A review of preliminary test-based statistical methods for the benefit of Six Sigma quality practitioners

Ravichandran

2010

Stat Papers

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“…Hence it is wise to adopt restricted estimation procedures when we have sufficient confidence in the prior information. Bancroft (1944) introduced the use of PTEs and eventually further advancements were proposed by Saleh and Sen (1978), Saleh and Kibria (1993), Kibria (2004), Saleh (2006), Kibria and Saleh (1993, 2004, 2005, 2006, 2010 and Tabatabaey (2014, 2015).…”

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

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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.

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“…This notion introduced the concept of preliminary test estimators to check the validity of our hypothesis on the parameter and also obtain more precise estimates. Bancroft (1944) introduced the use of PTES and eventually further advancements were proposed by Saleh and Sen (1978), Saleh and Kibria (1993), Kibria (2004), Saleh (2006), Kibria and Saleh (1993, 2004, 2005, 2010 and Tabatabaey (2014, 2015). Until now in the literature of inferential statistics, the researchers have developed PTES of the parameters of different distributions.…”

Section: Introductionmentioning

confidence: 99%

On the Construction of Preliminary Test Estimators of the Reliability Characteristics for the Exponential Distribution Based on Records

Chaturvedi

Malhotra

2018

American Journal of Mathematical and Management Sciences

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The one-parameter exponential distribution plays an important role in reliability theory. Two measures of reliability for exponential distribution are considered, and Sometimes, due to past knowledge or experience, the experimenter may be in a position to make an initial guess on some of the parameters of interest. In such cases, we can provide an improved estimator by incorporating the prior information on the parameters. Preliminary test estimators (PTES) have been developed in the literature for the parameters of various distributions. To the best of the knowledge of the authors, PTES are not available for and . For record values from exponential distribution, we define PTES based on uniformly minimum variance unbiased estimator (UMVUE), maximum likelihood estimator (MLE) and empirical Bayes estimator (EBE) for the powers of the parameter, and . Bias and mean square error (MSE) expressions for the proposed estimators are derived. A comparative study of different methods of estimation is done through simulation and it is established that PTES perform better than ordinary UMVUES, MLES and EBES.

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Preliminary test estimation of the parameters of exponential and Pareto distributions for censored samples

Cited by 22 publications

References 18 publications

A review of preliminary test-based statistical methods for the benefit of Six Sigma quality practitioners

A review of preliminary test-based statistical methods for the benefit of Six Sigma quality practitioners

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

On the Construction of Preliminary Test Estimators of the Reliability Characteristics for the Exponential Distribution Based on Records

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