Samir K. Bhattacharya

E-IG Model in Life Testing

A model for life time distribution, obtained by compounding the exponential distribution by the Inverse Gaussian distribution, has been studied.

Bayesian survival analysis based on the Rayleigh model

SummaryIn this paper, the Bayesian analysis of the survival data arising from a Rayleigh model is carried out under the assumption that the clinical study based onn patients is terminated at thedth death, for some preassignedd(0<d<-n), r resulting in the survival timest1≤t2≤...≤td, and (n-d) survivors. For the prior knowledge about the Rayleigh parameter, the gamma density, the inverted gamma density, and the beta density of the second kind are respectively assumed, and for each of these prior densities, the Bayes estimators of the mean survival time, the hazard function, and the survival function are obtained by assuming the usual squared error loss function. Finally, the analysis is extended to situations wherein the exact survival time is not available for any patient but only the deaths in given time intervals are recorded. The computations are illustrated by a numerical example.

Bayesian estimation for the Pareto income distribution

The Bayes estimators of the Gini index, the mean income and the proportion of the population living below a prescribed income level are obtained in this paper on the basis of censored income data from a pareto income distribution. The said estimators are obtained under the assumptions of a two-parameter exponential prior distribution and the usual squared error loss function. This work is also extended to the case when the income data are grouped and the exact incomes for the individuals in the population are not available. The method for the assessment of the hyperparameters is also outlined. Finally, the results are generalized for the doubly truncated gamma prior distribution.

Bayesian estimation of the Gini index for the PID

SummaryIn this paper, the Bayes estimators of the Gini index, the mean income and the proportion of the population living below a prescribed income level are obtained on the basis of censored income data from a Pareto income distribution (PID) under the assumption of the usual squared-error loss function (SELF) and truncated Erlang prior density (TEPD) for the underlying parameter. This work is also extended to the case when the income data are grouped and the exact earnings for the individual members of the population are not available.

Bayesian analysis of the mixture of exponential failure distributions

Abstract In this paper, a Bayesian reliability analysis is carried out for the mixture of two exponential failure distributions on the basis of failure time data x 1 x 2 x r , for a preassigned r , and ( n − r ) survivors from this mixed failure model. Under the assumptions of the squared error loss function (SELF) and suitable prior densities on the underlying parameter space, exact results for the Bayes estimators of the mean life and the reliability function are obtained.

Bayesian normal analysis with an inverse Gaussian prior

SummaryThis paper considers the Bayesian analysis of normal distribution when its variance has an inverse Gaussian prior density. The result is also generelized in a theorem that is subsequently presented.

Occupation times for two-state Markov chains

Abstract For a two-state Markov chain explicit results are derived for the distribution of the number of visits to state j during the time-interval (1,n], given that the initial state (at time 0) was i. The proof is based on combinatorial results of partition theory.

Life Estimation after Testing for Early Failures

Life estimation based on ordered observations from the exponential distribution is considered for the case when several early failures may be present. The method proposed here requires a preliminary statistical test to decide whether the suspected observations are indeed early failures. The role of the suspected observations (early failures) in the subsequent estimation problem is based on the result of this test. The proposed estimator has, under certain conditions, smaller mean square error than that of the minimum variance unbiased estimator, and its bias remains small.

Pretest estimation for some discrete distributions

This paper considers pretest estimation of the parameters of the binomial, the Poisson and the negative binomial distributions. It is assumed that a prior point estimate of the unknown parameter is available, and this value is tested as a preliminary hypothesis by considering a suitable randomized test. Depending on the result of this test, suitable estimators of the underlying parameter are chosen. The exact results for the bias and the mean squared error of the proposed estimators are obtained, and the computations are illustrated by numerical examples.

Bayesian reliability analysis when multiple early failures may be present

SummaryThis paper discusses the Bayesian reliability analysis for an exponential failure model on the basis of some ordered observations when the firstp observations may represent “early failures” or “outliers”. The Bayes estimators of the mean life and reliability are obtained for the underlying parametric model referred to as theSB(p) model under the assumption of the squared error loss function, the inverted gamma prior for the scale parameter and a generalized uniform prior for the nuisance parameter.