Calcutta Statistical Association Bulletin

The inequality of Kolmogorov (Sankhya, 1963) has been extended to a sequence of independent sub-Gaussian and other random variables. All the earlier results in the literature on this problem concerned only on the very special case of Bernoulli variables. We use martingale inequalities to establish a key result. A similar inequality is also proved for U-statistics based on exchangeable random variables.

Selection of the Lomax model through characterization results from amongst the class of continuous mixtures of exponential distributions has been examined. Properties covered are in main based on crude measures of hazard rate and mean residual life. Some closure properties have also been used for this purpose.

In this paper we discuss the issue of efficiency of a ranked set sample compared to a simple random sample in the context of a variety of parametric estimation problems. We establish that the use of appropriate variations of a ranked set sample often results in improved estimation of many common parameters of interest with a substantially smaller number of measurements compared to a simple random sample.

The results of Chatterjee and Chanopadhyay (1990) are extended here to the case where nuisance parameters are present. The extension involves the inclusion of the nuisance parameter alongwith the partial ancillary statistic in the loss functions. It is shown that the usual best conditional test is actually unconditionally optimum irrespective of any knowledge about the nuisance parameter. Some standard examples are considered where loss functions can be so chosen as to realise certain intuitively reasonable properties.

A necessary and sufficient condition is given so that the second order probability matching priors based on posterior quantiles will be the priors under which the Bayesian and frequentist Bartlett corrected conditional likelihood ratio statistics differ by 0(l). Several examples are given to illustrate the idea.

The present paper provides a nonpararnetric test procedure for comparing two treatments in clinical trials by using a sampling design which allocates more patients to the better treatment in course of decision making. Some exact and asymptotic results related to the performance characteristics and the properties of the proposed test are discussed and examined. Finally, the performance characteristics of the test are compared numerically with its possible competitors.

Recently, some interest has been focussed on the estimation of component life time distributions in coherent systems. For simplicity, most of the work assume independence between different component life times. Also, some specific dependence structure has been dealt with in some limited cases. In this work, we introduce a unified way of modelling the component life time distributions in a coherent system through the framework of multivariate failure times, which includes some arbitrary nature of dependence. Under independence, both parametric and nonparametric estimation of component life time distributions are discussed with continuous monitoring data and autopsy data as well. A specific dependence structure is also considered for this purpose.

A class of Row-Column Designs (RC-designs) in t + t_l-1 (t = t₁t₂) treatments has been constructed by supplementing a latin square type RC-design in t-1 treatments arranged in t x t array with principal diagonal (left to right) blank and having each treatment once in each row and once in each column. The blank diagonal positions are supplemented by t₁ new treatments each replicated t₂ times. These designs are simple partially efficiency balanced Row-Column designs (SPEB-RC-designs) having two sets of treatments with different number of replications. These designs are very useful in agricultural experiments particularly in plant development programme where limited seed material is available for new strains or varieties (t₁) as compared to standard or check varieties (t-1), already in existence.

Method of construction of main effect plans (saturated and unsaturated) through BIB designs, using necessary and sufficient condition of proportional frequencies, is proposed. Using this condition, we obtain two new plans 2¹⁶/18 and 2²⁵/27 not reported earlier. Utilising these plans, we have obtained two new asymmetrical orthogonal main effect plans.

Here we consider a two-component system where the components are identical but do not work independently within the system. Assuming the joint distribution of component lives to be Bivariate Exponential (BVED), system (series, parallel or stand-by) life distribution comes out to be a proper mixture of x²-distributions. We approximate the system life distribution as a chi-square with a multiplier that depends on system configuration. Prediction intervals for a single future observation (on component life) are constructed on the basis of system life observations. Further, we have taken Gamma and Rectangular priors for the parameters of the BVED and have approximated the unconditional distribution of system life as Beta with suitable parameters. Taking logarithmic transformation, we get Bayesian prediction intervals.