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The paper deals with the problem of predicting, on the basis of an observed sample from an inverse Gaussian distribution, a single future observation; as well as the mean of a set of future observations from the same distribution when guess values of the parameters are available. Using the general class of a prior which places a constant weight on the guess values, the paper derives the predictive p.d.f. and hence the prediction limits. The behaviour of the proposed limits as compared with the Padgett approximate classical limits [W. J. Padgett, J. Statist. Comput. Simul. 14 , 291–299 (1982)] is studied using an example. The proposed limits are found to be better than the classical limits.

In this paper an attempt is made to provide a method of obtaining the HPD-intervals for the scale and shape parameters of the Weibull distribution, when a prior distribution of the parameter places a weight (1 − b ) on the guess value of the parameter and distributes the rest probability mass b according to some specified distribution. The equal tail credible intervals have been obtained and it is proposed that these limits be used as initial points for obtaining the HPD-intervals.

The paper deals with the problem of estimation of exponential parameters when a guessed estimate of a location parameter is available. The Bayes estimators of the parameters, with suitably chosen prior distributions, have been obtained and are compared with the corresponding maximum likelihood estimators and uniformly minimum variance unbiased estimators on the basis of a Monte Carlo study of 1000 samples.

A modified likelihood ratio criterion is provided to discriminate between gamma and exponential distributions for a complete sample of life data. Estimates of the probability of correct selections have been obtained on the basis of a Monte Carlo study. A set of adaptive estimators for the shape and scale parameters are proposed and their efficiencies are studied on the basis of generated data.

This paper deals with the problem of average life estimation when the life times follow negative exponential distribution. A minimum mean square error estimator belonging to the class of linear combination of complete sufficient statistics has been obtained. The estimator thus obtained requires knowledge of coefficient of variation. The effect of using a guessed value of coefficient of variation on the estimator has also been studied.

An estimation procedure using a preliminary test of significance for the estimation of average life of life data has been discussed. The bias and mean square error of the estimators obtained by this procedure have been studied. The procedure has been illustrated by an example.

Necessary and sufficient condition for admissibility of a test procedure based on preliminary test of significance for life data has been obtained.