Modelling lifetimes by quantile functions using Parzen's score function

The present paper introduces methods of constructing quantile functions as models of lifetimes with monotone and nonmonotone hazard functions. This is accomplished on the basis of the relationships the hazard quantile function has with the score function introduced by Parzen in connection with the tail heaviness of probability distributions. Three models illustrated here contain several existing models as particular cases. The appropriateness of the models in real situations is also demonstrated.     

Bayesian Approach to Multicentre Sparse Data

In a 2 × 2 contingency table, when the sample size is small, there may be a number of cells that contain few or no observations, usually referred to as sparse data. In such cases, a common recommendation in the conventional frequentist methods is adding a small constant to every cell of the observed table to find the estimates of the unknown parameters. However, this approach is based on asymptotic properties of the estimates and may work poorly for small samples. An alternative approach would be to use Bayesian methods in order to provide better insight into the problem of sparse data coupled with fewer centers, which would otherwise be difficult to carry out the analysis. In this article, an attempt has been made to use hierarchical Bayesian model to a multicenter data on the effect of a surgical treatment with standard foot care among leprosy patients with posterior tibial nerve damage which is summarized as seven 2 × 2 tables. Monte Carlo Markov Chain (MCMC) techniques are applied in estimating the parameters of interest under sparse data setup.     

Some applications of lagrangian distributions in queueing theory and epidemiology

In this note we demonstrate that the Lagrangian distributions have applications in queueing theory and theory of epidemics. The Lagrangian distribution appears as the distribution describing the number of customers served in a busy period under certain conditions. Also, the Lagrangian distribution describes the distribution of number of persons infected by a certain infectious disease.     

Admissibility of generalized bayes and pitman estimates in the non-regular family

In this paper we have considered the problem of finding admissible estimates for a fairly general class of parametric functions in the so called “non-regular” type of densities Following Karlin s (1958) technique, we have established the ad-missibility of generalized Bayes estimates and Pitman estimates. Some examples are discussed.     

Scheduling material handling vehicles in a container terminal

Increasing global trade has created the need for efficient container ports. The goal of the port is to move containers as quickly as possible and at the least possible cost. Goods that are delayed at the port are inevitably tardy when delivered to the customer, and thus sanctioned by late charges. Two key activities in the port are (i) unloading of containers from truck and then storage in the export area, and (ii) removal of containers from import storage and then loading onto the trucks. Since containers are large and heavy, specialized material handling vehicles are required for transporting them within the terminal. The focus of this paper is on port terminals where straddle carriers are primarily used to move containers. Container terminals typically have well developed computer and communication networks. Through these networks a terminal scheduler will control and schedule the movement of the straddle carrier fleet in real time. The objective of the terminal scheduler is to minimize the empty travel of straddle carriers, while at the same time minimizing any delays in servicing customers. This paper presents a straddle scheduling procedure that can be used by a terminal scheduler to control the movement of straddle carriers. At its core, the procedure is driven by an assignment algorithm that dynamically matches straddle carriers and trucks, as each becomes available. The procedures were developed and tested in collaboration with the largest container terminal operator in the Port of New York and New Jersey. Using a simulation model of the real system, the superiority of the proposed procedure over two alternative scheduling strategies is illustrated.     

Testing equality of conditionally jfclhwdqw exponential distributions

For the models given V = v (a common random stress), X and Y are independently exponentially distributed with failure rates λ₁and λ₂v, testing H₀λ₁λ₂using a random ‘paired’ sample is considered. It is shown that a uniformly most powerful invariant test does not exist even for one sided alternatives; locally most powerful invariant tests are derived and compared with existing procedures. The method is illustrated with reliability data. Finally, the robustness of the tests when the relationships of the failure rates to V is more complex are established.     

An empirical model to predict arsenic pollution affected life expectancy

A robust, globally implementable and simple empirical model to predict the arsenic pollution affected life expectancy using a stepwise regression was developed. Life expectancy calculated using a life table technique requires crude death rates data that are not available for small administrative units, complex calculations and does not consider socioeconomic parameters. Hence, a model was needed to forecast the impact of arsenic pollution and socioeconomic parameters on life expectancy for locations with limited data availability. A linear multiple regression technique was used to develop an empirical model to predict arsenic pollution affected life expectancy at birth. The model was calibrated using nine arsenic polluted administrative blocks of district Murshidabad, West Bengal, India and tested independently for three other arsenic polluted blocks of the same district. The R ² values for the plot of actual versus predicted life expectancy at birth were 0.98 for calibration, testing and independent validation. The model is complementary to the life table technique and offers a means to assist planning by public health engineers and health policy makers to mitigate arsenic pollution on a community priority basis.     

“The Past in the Present: Mills,Tocqueville and the Necessity of History”

Historical sociology has achieved a reasonable degree of respectability in the discipline, and there is much interesting work being produced. But a pronounced aspect of much of this work is an indifference to the question of the value of studying the past as a way to understanding the present. This article argues that, rather than trying to outdo the historians by producing “better,” more theoretically sophisticated history, sociologists would better advance the case for historical sociology by showing how any particular historical study helps illuminate contemporary concerns. The article draws upon the writings of C. Wright Mills and Alexis de Tocqueville to show not just the need for historical sociology but also as indications of how this might best be done.     

Robustness of tests for directional mean

In this paper we study the robustness of the likelihood ratio, circular mean and circular trimmed mean test functionals in the context of tests of hypotheses regarding the mean direction of circular normal and wrapped normal distributions. We compute the level and power breakdown properties of the three test functionals and compare them. We find that the circular trimmed mean test functional has the best robustness properties for both the above-mentioned distributions. The level and power properties of the test statistics corresponding to these functionals are also studied. Two examples with real data are given for illustration. We also consider the problem of testing the mean direction of the von-Mises–Fisher distribution on the unit sphere and explore the robustness properties of the spherical mean direction and likelihood ratio test functionals.