133 research outputs found
Estimation of Inverse Weibull Distribution Under Type-I Hybrid Censoring
The hybrid censoring is a mixture of Type I and Type II censoring schemes.
This paper presents the statistical inferences of the Inverse Weibull
distribution when the data are Type-I hybrid censored. First we consider the
maximum likelihood estimators of the unknown parameters. It is observed that
the maximum likelihood estimators can not be obtained in closed form. We
further obtain the Bayes estimators and the corresponding highest posterior
density credible intervals of the unknown parameters under the assumption of
independent gamma priors using the importance sampling procedure. We also
compute the approximate Bayes estimators using Lindley's approximation
technique. We have performed a simulation study and a real data analysis in
order to compare the proposed Bayes estimators with the maximum likelihood
estimators.Comment: This paper is under review in the Austrian Journal of Statistics and
will likely be published ther
On the Sample Information About Parameter and Prediction
The Bayesian measure of sample information about the parameter, known as
Lindley's measure, is widely used in various problems such as developing prior
distributions, models for the likelihood functions and optimal designs. The
predictive information is defined similarly and used for model selection and
optimal designs, though to a lesser extent. The parameter and predictive
information measures are proper utility functions and have been also used in
combination. Yet the relationship between the two measures and the effects of
conditional dependence between the observable quantities on the Bayesian
information measures remain unexplored. We address both issues. The
relationship between the two information measures is explored through the
information provided by the sample about the parameter and prediction jointly.
The role of dependence is explored along with the interplay between the
information measures, prior and sampling design. For the conditionally
independent sequence of observable quantities, decompositions of the joint
information characterize Lindley's measure as the sample information about the
parameter and prediction jointly and the predictive information as part of it.
For the conditionally dependent case, the joint information about parameter and
prediction exceeds Lindley's measure by an amount due to the dependence. More
specific results are shown for the normal linear models and a broad subfamily
of the exponential family. Conditionally independent samples provide relatively
little information for prediction, and the gap between the parameter and
predictive information measures grows rapidly with the sample size.Comment: Published in at http://dx.doi.org/10.1214/10-STS329 the Statistical
Science (http://www.imstat.org/sts/) by the Institute of Mathematical
Statistics (http://www.imstat.org
Predicting Failure times for some Unobserved Events with Application to Real-Life Data
This study aims to predict failure times for some units in some lifetime experiments. In some practical situations, the experimenter may not be able to register the failure times of all units during the experiment. Recently, this situation can be described by a new type of censored data called multiply-hybrid censored data. In this paper, the linear failure rate distribution is well-fitted to some real-life data and hence some statistical inference approaches are applied to estimate the distribution parameters. A two-sample prediction approach applied to extrapolate a new sample simulates the observed data for predicting the failure times for the unobserved units
Maximum Likelihood Estimation for Length biased Burr- XII Distribution with Censored Sample
In this paper, defined by [1],the maximum likelihood estimation for the parameters of the LBB-XII distribution are studied.Also, different types of censoring, such as, type I, type II. A simulation study is perform to evaluate the maximum likelihood estimates
Pareto Distribution under Hybrid Censoring: Some Estimation
In the present study, the Pareto model is considered as the model from which observations are to be estimated using a Bayesian approach. Properties of the Bayes estimators for the unknown parameters have studied by using different asymmetric loss functions on hybrid censoring pattern and their risks have compared. The properties of maximum likelihood estimation and approximate confidence length have also been investigated under hybrid censoring. The performances of the procedures are illustrated based on simulated data obtained under the Metropolis-Hastings algorithm and a real data set
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