Calcutta Statistical Association Bulletin

The paper proposes a general hierarchical Bayesian methodology for the analysis of binary longitudinal data. The Bayesian method is implemented via Markov Chain Monte Carlo (MCMC) integration technique and is applied to a real dataset which was collected to study stereotyped behavior in deer mice.

A reliability setting is considered for comparing two competing equipments based on a fixed number of observations. A two stage failure censored design is proposed in which a preassigned number of items are randomised equally at the first stage and the better items are examined exclusively at the end of the second stage. Here at each stage, we consider type II censoring (see e.g. Miller (1981)) . That is, observations are made upto a common prefixed proportion of failures at each stage. For exponential responses, the exact bias and variance of the estimated failure rate difference at the end of the trial are derived. Competitors of the proposed procedure are also suggested. Some asymptotics related to all these procedures are also obtained.

We consider a generalized linear model with canonical link when some of the covariates are subject to measurement error. In this article we propose a likelihood based method of adjusting the estimate of the regression parameter β by replacing normal measurment error distribution with a larger and flexible class of parametric distributions in order to get obust estimates of the regression parameter. We replace the normal measurement error model with the multivariate measurement error model. We also investigate the robustness of normal measurement error model against nonnormality. We show by conducting a simulation study that the maximum likelihood estimator of the regression parameter β in a logistic regression obtained under the assumption of normal measurement error performs poorly compared to the estimator obtained by assuming t measurement error when the true measurement error model is a t-distribution with known kurtosis parameter. The likelihood estimates are obtained by applying EM alogrithm instead of directly maximizing the likelihood function which involves evaluation of a high dimensional integral and in most situations it is unmanageable.

The asymptotic distribution of the test statistic proposed by Al-Shiha and Yang (1999) for analyzing nonreplicated factorials is deril- ed for large sample sizes. An extensive study is presented to compare the asymptotic percentiles with the empirical percentiles of the test statistic.

The purpose of this paper is to suggest two classes of block designs having orthogonal factorial structure (O.F.S.)

We study two models of a single server queue with vacations. In model A, we study an M ⁄ M ⁄1 queue with deterministic vacations and designate it as M⁄M⁄D⁄l queue and in model B we study an M⁄D⁄1 queue with exponential vacations and designate it as M⁄D⁄M⁄1 queue. We obtain time dependent as well as steady state probability generating functions for both the models. For the steady state, we obtain explicit results for the mean number in the system and the mean waiting times for both models. All known results of the M ⁄ M ⁄1 and the M⁄D⁄1 queues are derived as special cases.

In successive sampling with partial replacement, an estimator is proposed for the population mean on the second of two successive occasions utilising information available on both the occasions on an auxiliary variate with an unknown population mean. It is shown that the proposed estimator is more efficient than the sample mean and the estimators considered by Sen (1971). An empirical study is also included.

A general class of distribution F(x) = ah(x) + b has been characterized by considering conditional moments of a function of two order statistics, conditioned on the pair of order statistics. Further, its important consequences are also discussed.

In this paper the estimation of a Location parameter with an asymmetric Linex loss function is discussed. The admissibility of best location-invariant estimator under Linex loss, which we refer to it as Pitmantype estimator, is proved.

In this note a subordinated process with Geometric Exponential operational time is introduced and studied.

Statewide assembly election was held in May 2001 in West Bengal, where an alliance of leftist political parties has been in power since 1977. All opinion and exit polls conducted in the state predicted a closely contested election with a very slim projected majority for the ruling alliance, if at all. The actual outcome was another landslide victory for them. This paper reviews these opinion and exit poll results and shows certain statistical inconsistencies in their projected figures. A brief analysis of 2001 election results reveals some statistically significant evidence for the presence of anti-incumbancy factor acting against the ruling alliance candidates. This analysis also indicates that there was no significant decrease in the fragmentation of opposition votes in 2001 election compared to the most recent assembly election in 1996 and the most recent parliamentary election in 1999.

We explore statistical independence and dynamical system structures in protein primary sequences, based on the Swiss-Prot database. Results of testing for independence vs. Markov dependence in each sequence are reported. As for the dynamical systems, we discuss the problems of formulating a suitable fractal dimension for discrete state-space and estimating the embedding dimension as well as the link function. Some descriptive statistics for the sequences are also given.