A two phases queueing system with Bernoulli vacation schedule under multiple vacation policy

This paper deals with a single server Poisson arrival queue with two phases of heterogeneous service along with a Bernoulli schedule vacation model, where after two successive phases service the server either goes for a vacation with probability p (0≤p≤1) or may continue to serve the next unit, if any, with probability q(=1−p). Further the concept of multiple vacation policy is also introduced here. We obtained the queue size distributions at a departure epoch and at a random epoch, Laplace Stieltjes Transform of the waiting time distribution and busy period distribution along with some mean performance measures. Finally we discuss some statistical inference related issues.     

A note on the queue with a random set-up time under a restricted admissibility policy with a Bernoulli vacation schedule

This paper deals with the queue size distribution of an M^x/G/1 queue with a random set-up time and with a Bernoulli vacation schedule under a restricted admissibility policy. This generalizes the model studied by Madan and Choudhury [Sankhyá 66 (2004) 175–193].     

The Impact of Family Planning on Fertility in a Rural Area of East Pakistan

This pape revaluates a family planning pilot project conducted by the Pakistan Academy for Rural Development in Comilla, East Pakistan. The evaluation is based upon an analysis of the extent to which adoption of conventional contraceptives (condoms and foam tablets) has reduced fertility in selected villages of the Comilla-Kotwali precinct, during the years 1962-66.The study was carried out by comparing adopter and non-adopter rates of pregnancy and analyzing the trends in pregnancy reduction that resulted from adoption. The findings indicate that (1) although the pregnancy rate of adopters has increased steadily throughout the time period, in 1966 the rate is still less than half of what was expected had adoption not occurred; (2) contraceptive use-effectiveness decreases with length of time of use; and (3) pregnancy reduction has been declining since 1964.     

A Fairly Accurate Approximation to the Area Under Normal Curve

In this article, we present a new approximation to the cumulative distribution function of standard normal distribution. The approximation is fairly accurate with minimum accuracy of seven decimal digits. To the best of our knowledge, this formula outperforms other such approximations available in literature.     

Parametric scalp mapping and inference via spatially smooth linear models for mismatch negativity studies

Mismatch negativity (MMN) is a neurophysiological tool that can be used to investigate various facets of comprehension. Subjects are presented with different stimuli to elicit the MMN response, which is derived from electroencephalography (EEG) signals recorded at electrodes across the brain. We propose a methodology to extend single electrode analyses of MMN data by generating smooth scalp maps of estimated experimental effects. It is shown that penalized least squares estimates of effect maps can be produced using a two step procedure involving (a) ANOVA at each electrode and (b) spatial smoothing across electrodes. A Fisher von-Mises kernel is used for smoothing scalp maps with cross-validated bandwidth selection. The methodology is applied to a case control study involving aphasics (language disordered individuals). Analysis of residuals shows possible heteroscedasticity and non-Gaussian tail behavior. For robust inference, a semiparametric multivariate approach is proposed to determine the significance of parametric maps. A variety of global and regional test statistics are developed to investigate the significance of spatial patterns in treatment effects. The methodology is seen to confirm previous findings from single electrode analysis and identifies some new significant spatial patterns of difference between controls and aphasics.     

A class of chain ratio–product type estimators with two auxiliary variables under double sampling scheme

In this paper, a chain ratio–product type estimators has been developed for estimating population mean of the study variable using two auxiliary variables under double sampling scheme, when the information on another additional auxiliary character is available along with the main auxiliary character. The optimum property of the proposed strategy has been identified in two different cases with their variances. Theoretical and empirical studies have been done to demonstrate the efficiency of the proposed estimator over other estimators, which utilized the information on two auxiliary characteristics.     

A Modular CDF Approach for the Approximation of Percentiles

This article describes a method for computing approximate statistics for large data sets, when exact computations may not be feasible. Such situations arise in applications such as climatology, data mining, and information retrieval (search engines). The key to our approach is a modular approximation to the cumulative distribution function (cdf) of the data. Approximate percentiles (as well as many other statistics) can be computed from this approximate cdf. This enables the reduction of a potentially overwhelming computational exercise into smaller, manageable modules. We illustrate the properties of this algorithm using a simulated data set. We also examine the approximation characteristics of the approximate percentiles, using a von Mises functional type approach. In particular, it is shown that the maximum error between the approximate cdf and the actual cdf of the data is never more than 1% (or any other preset level). We also show that under assumptions of underlying smoothness of the cdf, the approximation error is much lower in an expected sense. Finally, we derive bounds for the approximation error of the percentiles themselves. Simulation experiments show that these bounds can be quite tight in certain circumstances.