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Full-Text Articles in Social and Behavioral Sciences
Bayesian And Semi-Bayesian Estimation Of The Parameters Of Generalized Inverse Weibull Distribution, Kamaljit Kaur, Kalpana K. Mahajan, Sangeeta Arora
Bayesian And Semi-Bayesian Estimation Of The Parameters Of Generalized Inverse Weibull Distribution, Kamaljit Kaur, Kalpana K. Mahajan, Sangeeta Arora
Journal of Modern Applied Statistical Methods
Bayesian and semi-Bayesian estimators of parameters of the generalized inverse Weibull distribution are obtained using Jeffreys’ prior and informative prior under specific assumptions of loss function. Using simulation, the relative efficiency of the proposed estimators is obtained under different set-ups. A real life example is also given.
Doubly Censored Data From Two-Component Mixture Of Inverse Weibull Distributions: Theory And Applications, Tabassum Sindhu, Navid Feroze, Muhammad Aslam
Doubly Censored Data From Two-Component Mixture Of Inverse Weibull Distributions: Theory And Applications, Tabassum Sindhu, Navid Feroze, Muhammad Aslam
Journal of Modern Applied Statistical Methods
Finite mixture distributions consist of a weighted sum of standard distributions and are a useful tool for reliability analysis of a heterogeneous population. They provide the necessary flexibility to model failure distributions of components with multiple failure models. The analysis of the mixture models under Bayesian framework has received sizable attention in the recent years. However, the Bayesian estimation of the mixture models under doubly censored samples has not yet been introduced in the literature. The main objective of this paper is to discuss the Bayes estimation of the inverse Weibull mixture distributions under doubly censoring. Different priors and loss …
Study Of The Left Censored Data From The Gumbel Type Ii Distribution Under A Bayesian Approach, Tabassum Naz Sindhu, Navid Feroze, Muhammad Aslam
Study Of The Left Censored Data From The Gumbel Type Ii Distribution Under A Bayesian Approach, Tabassum Naz Sindhu, Navid Feroze, Muhammad Aslam
Journal of Modern Applied Statistical Methods
Based on left type II censored samples from a Gumbel type II distribution, the Bayes estimators and corresponding risks of the unknown parameter were obtained under different asymmetric loss functions, assuming different informative and non-informative priors. Elicitation of hyper-parameters through prior predictive approach has also been discussed. The expressions for the credible intervals and posterior predictive distributions have been derived. Comparisons of these estimators are made through simulation study using numerical and graphical methods.
Bayesian Estimation Of The Parameters Of Two-Component Mixture Of Rayleigh Distribution Under Doubly Censoring, Tahassum N. Sindhu, Navid Feroze, Muhammad Aslam
Bayesian Estimation Of The Parameters Of Two-Component Mixture Of Rayleigh Distribution Under Doubly Censoring, Tahassum N. Sindhu, Navid Feroze, Muhammad Aslam
Journal of Modern Applied Statistical Methods
Recently, the Bayesian analysis of the two-component mixture of lifetime models under singly type I censored samples was discussed. The Bayes estimation of the parameters of mixture of two Rayleigh distributions (MTRD) is developed under doubly censoring. Different informative priors, under squared error loss function and k-loss function, have been assumed for the posterior estimation. The performance of different estimators has been compared in terms of posterior risks by analyzing the simulated and real life data sets.
On Bayesian Estimation And Predictions For Two-Component Mixture Of The Gompertz Distribution, Navid Feroze, Muhammad Aslam
On Bayesian Estimation And Predictions For Two-Component Mixture Of The Gompertz Distribution, Navid Feroze, Muhammad Aslam
Journal of Modern Applied Statistical Methods
Mixtures models have received sizeable attention from analysts in the recent years. Some work on Bayesian estimation of the parameters of mixture models have appeared. However, the were restricted to the Bayes point estimation The methodology for the Bayesian interval estimation of the parameters for said models is still to be explored. This paper proposes the posterior interval estimation (along with point estimation) for the parameters of a two-component mixture of the Gompertz distribution. The posterior predictive intervals are also derived and evaluated. Different informative and non-informative priors are assumed under a couple of loss functions for the posterior analysis. …
New Approximate Bayesian Confidence Intervals For The Coefficient Of Variation Of A Gaussian Distribution, Vincent A. R. Camara
New Approximate Bayesian Confidence Intervals For The Coefficient Of Variation Of A Gaussian Distribution, Vincent A. R. Camara
Journal of Modern Applied Statistical Methods
Confidence intervals are constructed for the coefficient of variation of a Gaussian distribution. Considering the square error and the Higgins-Tsokos loss functions, approximate Bayesian models are derived and compared to a published classical model. The models are shown to have great coverage accuracy. The classical model does not always yield the best confidence intervals; the proposed models often perform better.
Approximate Bayesian Confidence Intervals For The Mean Of A Gaussian Distribution Versus Bayesian Models, Vincent A. R. Camara
Approximate Bayesian Confidence Intervals For The Mean Of A Gaussian Distribution Versus Bayesian Models, Vincent A. R. Camara
Journal of Modern Applied Statistical Methods
This study obtained and compared confidence intervals for the mean of a Gaussian distribution. Considering the square error and the Higgins-Tsokos loss functions, approximate Bayesian confidence intervals for the mean of a normal population are derived. Using normal data and SAS software, the obtained approximate Bayesian confidence intervals were compared to a published Bayesian model. Whereas the published Bayesian method is sensitive to the choice of the hyper-parameters and does not always yield the best confidence intervals, it is shown that the proposed approximate Bayesian approach relies only on the observations and often performs better.
Approximate Bayesian Confidence Intervals For The Mean Of An Exponential Distribution Versus Fisher Matrix Bounds Models, Vincent A. R. Camara
Approximate Bayesian Confidence Intervals For The Mean Of An Exponential Distribution Versus Fisher Matrix Bounds Models, Vincent A. R. Camara
Journal of Modern Applied Statistical Methods
The aim of this article is to obtain and compare confidence intervals for the mean of an exponential distribution. Considering respectively the square error and the Higgins-Tsokos loss functions, approximate Bayesian confidence intervals for parameters of exponential population are derived. Using exponential data, the obtained approximate Bayesian confidence intervals will then be compared to the ones obtained with Fisher Matrix bounds method. It is shown that the proposed approximate Bayesian approach relies only on the observations. The Fisher Matrix bounds method, that uses the z-table, does not always yield the best confidence intervals, and the proposed approach often performs better.
Bayesian Reliability Modeling Using Monte Carlo Integration, Vincent A. R. Camara, Chris P. Tsokos
Bayesian Reliability Modeling Using Monte Carlo Integration, Vincent A. R. Camara, Chris P. Tsokos
Journal of Modern Applied Statistical Methods
Bayesian Reliability Modeling Using Monte Carlo IntegrationThe aim of this article is to introduce the concept of Monte Carlo Integration in Bayesian estimation and Bayesian reliability analysis. Using the subject concept, approximate estimates of parameters and reliability functions are obtained for the three-parameter Weibull and the gamma failure models. Four different loss functions are used: square error, Higgins-Tsokos, Harris, and a logarithmic loss function proposed in this article. Relative efficiency is used to compare results obtained under the above mentioned loss functions.
Approximate Bayesian Confidence Intervals For The Variance Of A Gaussian Distribution, Vincent A. R. Camara
Approximate Bayesian Confidence Intervals For The Variance Of A Gaussian Distribution, Vincent A. R. Camara
Journal of Modern Applied Statistical Methods
The aim of the present study is to obtain and compare confidence intervals for the variance of a Gaussian distribution. Considering respectively the square error and the Higgins-Tsokos loss functions, approximate Bayesian confidence intervals for the variance of a normal population are derived. Using normal data and SAS software, the obtained approximate Bayesian confidence intervals will then be compared to the ones obtained with the well known classical method. The Bayesian approach relies only on the observations. It is shown that the proposed approximate Bayesian approach relies only on the observations. The classical method, that uses the Chi-square statistic, does …