scholarly journals Estimation of Parameters of Generalized Inverted Exponential Distribution for Progressive Type-II Censored Sample with Binomial Removals

2013 ◽  
Vol 2013 ◽  
pp. 1-12 ◽  
Author(s):  
Sanjay Kumar Singh ◽  
Umesh Singh ◽  
Manoj Kumar
Keyword(s):  
Maximum Likelihood ◽  
Exponential Distribution ◽  
Estimation Procedure ◽  
Model Parameters ◽  
Type Ii ◽  
Bayes Estimators ◽  
Estimation Of Parameters ◽  
Data Set ◽  
Progressive Type ◽  
Censored Sample

We obtained the maximum likelihood and Bayes estimators of the parameters of the generalized inverted exponential distribution in case of the progressive type-II censoring scheme with binomial removals. Bayesian estimation procedure has been discussed under the consideration of the square error and general entropy loss functions while the model parameters follow the gamma prior distributions. The performances of the maximum likelihood and Bayes estimators are compared in terms of their risks through the simulation study. Further, we have also derived the expression of the expected experiment time to get a progressively censored sample with binomial removals, consisting of specified number of observations from generalized inverted exponential distribution. An illustrative example based on a real data set has also been given.

scholarly journals Statistical inference for Kumaraswamy-exponential distribution based on progressive Type-II censored data with binomial removals

2020 ◽  
Vol 53 (2) ◽  
pp. 147-163
Author(s):  
RAKHI MOHAN ◽  
MANOJ CHACKO
Keyword(s):  
Exponential Distribution ◽  
Loss Function ◽  
Real Data ◽  
Maximum Likelihood Estimates ◽  
Type Ii ◽  
Bayes Estimators ◽  
Estimation Of Parameters ◽  
Unknown Parameters ◽  
Data Set ◽  
Better Than

In this paper, estimation of parameters of Kumaraswamy-exponential distribution with shape parameters α and β is considered based on a progressively type-II censored sample with binomial removals. Together with the unknown parameters, the removal probability p is also estimated. Bayes estimators are obtained using different loss functions such as squared error, LINEX loss function and entropy loss function. All Bayesian estimates are compared with the corresponding maximum likelihood estimates numerically in terms of their bias and mean square error values and found that Bayes estimators perform better than MLE’s for β and p and MLEs perform better than Bayes estimators for α. A real data set is also used for illustration.

scholarly journals Progressive Type-II Censoring Schemes of Extended Odd Weibull Exponential Distribution with Applications in Medicine and Engineering

Mathematics ◽  
2020 ◽  
Vol 8 (10) ◽  
pp. 1679
Author(s):  
R. Alshenawy ◽  
Ali Al-Alwan ◽  
Ehab M. Almetwally ◽  
Ahmed Z. Afify ◽  
Hisham M. Almongy
Keyword(s):  
Maximum Likelihood ◽  
Exponential Distribution ◽  
Confidence Intervals ◽  
Estimation Methods ◽  
Model Parameters ◽  
Type Ii ◽  
Type Ii Censoring ◽  
Progressive Type ◽  
Censoring Scheme ◽  
Progressive Type Ii Censoring

In this paper, the parameters of the extended odd Weibull exponential distribution are estimated under progressive type-II censoring scheme with random removal. The model parameters are estimated using the maximum product spacing and maximum likelihood estimation methods. Further, we explore the asymptotic confidence intervals and bootstrap confidence intervals for the model parameters. Monte Carlo simulations are performed to compare between the proposed estimation methods under progressive type-II censoring scheme. An empirical study using two real datasets form engineering and medicine fields to validate the introduced methods of inference. Based on our study, we can conclude that the maximum product of spacing method outperforms the maximum likelihood method for estimating the extended odd Weibull exponential (EOWE) parameters under a progressive type-II censoring scheme in both numerical and empirical cases.

scholarly journals Bayesian Estimation for Inverse Weibull Distribution Under Progressive Type-II Censored Data With Beta-Binomial Removals

2018 ◽  
Vol 47 (1) ◽  
pp. 77-94
Author(s):  
Pradeep Kumar Vishwakarma ◽  
Arun Kaushik ◽  
Aakriti Pandey ◽  
Umesh Singh ◽  
Sanjay Kumar Singh
Keyword(s):  
Weibull Distribution ◽  
Real Data ◽  
Estimation Procedure ◽  
Type Ii ◽  
Unknown Parameters ◽  
Data Set ◽  
Progressive Type ◽  
Inverse Weibull Distribution ◽  
Type Ii Censored Data ◽  
Censoring Scheme

This paper deals with the estimation procedure for inverse Weibull distribution under progressive type-II censored samples when removals follow Beta-binomial probability law. To estimate the unknown parameters, the maximum likelihood and Bayes estimators are obtained under progressive censoring scheme mentioned above. Bayes estimates are obtained using Markov chain Monte Carlo (MCMC) technique considering square error loss function and compared with the corresponding MLE's. Further, the expected total time on test is obtained under considered censoring scheme.  Finally, a real data set has been analysed to check the validity of the study.

scholarly journals Generalized Weighted Rama Distribution: Properties and Application to Model Lifetime Data

2021 ◽  
pp. 9-37
Author(s):  
Samuel U. Enogwe ◽  
Chisimkwuo John ◽  
Happiness O. Obiora-Ilouno ◽  
Chrisogonus K. Onyekwere
Keyword(s):  
Maximum Likelihood ◽  
Likelihood Estimation ◽  
Real Data ◽  
Maximum Likelihood Estimates ◽  
Model Parameters ◽  
Data Sets ◽  
Estimation Of Parameters ◽  
Data Set ◽  
Bathtub Shape ◽  
Asymptotic Confidence Intervals

In this paper, we propose a new lifetime distribution called the generalized weighted Rama (GWR) distribution, which extends the two-parameter Rama distribution and has the Rama distribution as a special case. The GWR distribution has the ability to model data sets that have positive skewness and upside-down bathtub shape hazard rate. Expressions for mathematical and reliability properties of the GWR distribution have been derived. Estimation of parameters was achieved using the method of maximum likelihood estimation and a simulation was performed to verify the stability of the maximum likelihood estimates of the model parameters. The asymptotic confidence intervals of the parameters of the proposed distribution are obtained. The applicability of the GWR distribution was illustrated with a real data set and the results obtained show that the GWR distribution is a better candidate for the data than the other competing distributions being investigated.

ON MODELING AND ANALYZING CORRUPTED RELIABILITY DATA

1995 ◽  
Vol 02 (03) ◽  
pp. 245-267
Author(s):  
A.J. WATKINS ◽  
R.M. GRIFFIN
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimator ◽  
Model Parameters ◽  
Data Recording ◽  
Estimation Of Parameters ◽  
Likelihood Estimator ◽  
Simulation Experiments ◽  
Reliability Data ◽  
Data Set ◽  
Underlying Distribution

This paper is concerned with the effect of various data recording errors on the estimation of parameters in models commonly used in the analysis of reliability data. We start by outlining sources of such errors, and propose some modeling strategies that allow these errors into the framework of our analysis. It is then shown that the estimation of model parameters needs to take into account a mis-specified model, with the consequence that any theoretical advantages nominally enjoyed by estimators are reduced. In particular, the results from a series of simulation experiments show that the maximum likelihood estimator is no longer asymptotically unbiased. We next outline an approach that generalizes the usual asymptotic theory to obtain expressions for both the mean and variance of the maximum likelihood estimator in the present framework; these expressions involve both the underlying distribution and parameters controlling the extent to which recording errors are present in a data set. We then link these expressions to results obtained in a series of simulation experiments, and show that this approach accommodates a general formulation of the effect of data recording errors. We conclude with a discussion of the practical consequences of this work.

Predicting the time of occurrence of decompression sickness

1992 ◽  
Vol 72 (4) ◽  
pp. 1541-1548 ◽  
Author(s):  
P. K. Weathersby ◽  
S. S. Survanshi ◽  
L. D. Homer ◽  
E. Parker ◽  
E. D. Thalmann
Keyword(s):  
Maximum Likelihood ◽  
Probabilistic Models ◽  
Decompression Sickness ◽  
Likelihood Estimation ◽  
Estimation Procedure ◽  
Model Parameters ◽  
Conditional Probabilities ◽  
Data Set ◽  
Additional Information ◽  
Use Of Knowledge

Probabilistic models and maximum likelihood estimation have been used to predict the occurrence of decompression sickness (DCS). We indicate a means of extending the maximum likelihood parameter estimation procedure to make use of knowledge of the time at which DCS occurs. Two models were compared in fitting a data set of nearly 1,000 exposures, in which greater than 50 cases of DCS have known times of symptom onset. The additional information provided by the time at which DCS occurred gave us better estimates of model parameters. It was also possible to discriminate between good models, which predict both the occurrence of DCS and the time at which symptoms occur, and poorer models, which may predict only the overall occurrence. The refined models may be useful in new applications for customizing decompression strategies during complex dives involving various times at several different depths. Conditional probabilities of DCS for such dives may be reckoned as the dive is taking place and the decompression strategy adjusted to circumstance. Some of the mechanistic implications and the assumptions needed for safe application of decompression strategies on the basis of conditional probabilities are discussed.

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