MAXIMUM LIKELIHOOD ESTIMATION AND BOOTSTRAP CONFIDENCE INTERVALS FOR A SIMPLE STEP-STRESS ACCELERATED GENERALIZED EXPONENTIAL MODEL WITH TYPE-II CENSORED DATA

2015 ◽  
Vol 50 (2) ◽  
pp. 111-124
Author(s):  
G. H. Abd El-Monem ◽  
Z. F. Jaheen
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Confidence Intervals ◽  
Censored Data ◽  
Likelihood Estimation ◽  
Exponential Model ◽  
Type Ii ◽  
Bootstrap Confidence Intervals ◽  
Type Ii Censored Data ◽  
Simple Step

Estimation of P(X

2017 ◽  
Vol 34 (7) ◽  
pp. 1111-1122 ◽  
Author(s):  
Soumya Roy ◽  
Biswabrata Pradhan ◽  
E.V. Gijo
Keyword(s):  
Maximum Likelihood ◽  
Censored Data ◽  
Quality Characteristic ◽  
Logistic Distribution ◽  
Type Ii ◽  
Finite Sample ◽  
Data Set ◽  
Content Type ◽  
Type Ii Censored Data ◽  
Interval Estimators

Purpose The purpose of this paper is to compare various methods of estimation of P(X<Y) based on Type-II censored data, where X and Y represent a quality characteristic of interest for two groups. Design/methodology/approach This paper assumes that both X and Y are independently distributed generalized half logistic random variables. The maximum likelihood estimator and the uniformly minimum variance unbiased estimator of R are obtained based on Type-II censored data. An exact 95 percent maximum likelihood estimate-based confidence interval for R is also provided. Next, various Bayesian point and interval estimators are obtained using both the subjective and non-informative priors. A real life data set is analyzed for illustration. Findings The performance of various point and interval estimators is judged through a detailed simulation study. The finite sample properties of the estimators are found to be satisfactory. It is observed that the posterior mean marginally outperform other estimators with respect to the mean squared error even under the non-informative prior. Originality/value The proposed methodology can be used for comparing two groups with respect to a suitable quality characteristic of interest. It can also be applied for estimation of the stress-strength reliability, which is of particular interest to the reliability engineers.

A New Approach to Estimating Populations by the Removal Method

1983 ◽  
Vol 40 (12) ◽  
pp. 2153-2169 ◽  
Author(s):  
Jon Schnute
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
New Brunswick ◽  
Population Size ◽  
Confidence Intervals ◽  
Likelihood Estimation ◽  
Data Interpretation ◽  
Population Estimate ◽  
New Approach ◽  
Removal Method

This paper presents a new approach to the use of removal data in estimating the size of a population of fish or other animals. The theory admits a variety of assumptions on how catchability varies among fishings including the assumption of constant catchability, which underlies most previous work. The methods here hinge on maximum likelihood estimation, and they can be used both to decide objectively if the data justify rejecting constant catchability and to determine confidence intervals for the parameters. The work includes a new method of assigning confidence to the population estimate and points out problems with methods currently available in the literature, even in the case of constant catchability. The theory is applied both to data in historical literature and to more recent data from streams in New Brunswick, Canada. These examples demonstrate that the assumption of constant catchability can frequently lead to serious errors in data interpretation. In some cases, the conclusion that the population size is well known may be blatantly false, and reasonable estimates may be impossible without further data.

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