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].     

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.     

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.     

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.     

Analysis of an unreliable MX/G1G2/1/repeated service queue with delayed repair under randomized vacation policy

Abstract

In this article we consider an unreliable M^X/G/1 queue with two types of general heterogeneous service and optional repeated service subject to server’s break down and delayed repair under randomized vacation policy. We assume that customer arrive to the system according to a compound Poisson process. The server provides two types of general heterogeneous service and a customer can choose either type of service before its service start. After the completion of either type of service, the customer has the further option to repeat the same type of service once again. While the server is working with any types of service or repeated service, it may breakdown at any instant. Further the concept of randomized vacation is also introduced. For this model, we first derive the joint distribution of state of the server and queue size by considering both elapsed and remaining time, which is one of the objective of this article. Next, we derive Laplace Stieltjes transform of busy period distribution. Finally, we obtain some important performance measure and reliability indices of this model.     

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.     

Relative income and fertility

The present study examines the relationship between relative income (i.e., actual income in relation to the expected income of one’s socioeconomic group) and fertility, using data collected by the 1967-1968Canadian Family Growth Study (Balakrishnan et al., 1975). We broaden the tests of relative income beyond cumulative fertility to spacing behavior and then examine some of the assumptions included in the relative income model of fertility. Results of the tests, in brief, are as follows: (a) Relative income is found to be more closely related to spacing than to cumulative fertility; and (b) the relationship between relative income and fertility is strongest among those couples who plan their life ahead and have a high level of education and occupation, and when temporal alignment is brought between the measures of relative income and fertility. For the relative income model to receive confirmation, it was specified that the following hypotheses must be confirmed: (a) that fertility behavior would vary positively with relative income but the fertility norm would show no relationship with relative income; and (b) that consumption norms and behavior would show no relationship with relative income. The outcome of these tests are in the expected direction, giving support to the relative income model. In addition, there is some evidence of predictive capability of the relative income model for correlative behavior.