On the Alias Method for Generating Random Variables from a Discrete Distribution

The alias method of Walker is a clever, new, fast method for generating random variables from an arbitrary, specified discrete distribution. A simple probabilistic proof is given, in terms of mixtures, that the method works for any discrete distribution with a finite number of outcomes. A more efficient version of the table-generating portion of the method is described. Finally, a brief discussion on efficiency of the method is given. We believe that the generality, speed, and simplicity of the method make it attractive for use in generating discrete random variables.     

Pooled Cross-Sectional and Time Series Data: A Survey of Current Statistical Methodology

A data base that provides a multivariate statistical history for each of a number of individual entities is called a pooled cross-sectional and time series data base in the econometrics literature. In marketing and survey literature the terms panel data or longitudinal data are often used. In management science a convenient term might be management data base. Such a data base provides a particularly rich environment for statistical analysis. This article reviews methods for estimating multivariate relationships particular to each individual entity and for summarizing these relationships for a number of individuals. Inference to a larger population when the data base is viewed as a sample is also considered.     

Generalized Linear Models

The importance of random number generators has increased over the years. This follows from the fact that contemporary research methods rely more and more on simulation and the increased importance of encryption technology. The output of a random number generator is created by either an algorithm or a physical device. The most popular method for random number generation is through the use of an algorithm. This article presents a new category of physical random bit generator that is packaged by several manufacturers. A statistical analysis of the output from the generators is given.     

Resolving the Mixed Models Controversy

Two standard mixed models with interactions are discussed. When each is viewed in the context of superpopulation models, the mixed models controversy is resolved. The tests suggested by the expected mean squares under the constrained-parameters model are correct for testing the main effects and interactions under both the unconstrained-and constrained-parameters models.     

Change-Point Estimation in Long Memory Nonparametric Models with Applications

We consider the estimation of a change point or discontinuity in a regression function for random design model with long memory errors. We provide several change-point estimators and investigate the consistency of the estimators. Using the fractional ARIMA process as an example of long memory process, we report a small Monte Carlo experiment to compare the performance of the estimators in finite samples. We finish by applying the method to a climatological data example.     

Effects of censoring on the robustness of exponential-based confidence intervals for median lifetime

Statistical procedures for constructing confidence intervals for median lifetime often rest on a distributional assumption for failure times.This paper explores the interplay between censoring levels and robustness for two construction procedures based on exponential lifetime, subject to general right-censoring. Data are simulated from nearby Weibull distributions. As expected, the simulations indicate that when the exponential assumption is not satisfied, observed coverage by the confidence intervals may differ substantially from the specified coverage level. The marked improvement in the robustness properties of the intervals as the level of censoring increases suggests questions for future research.     

On the asymptotic properties of parameter estimates in a regression model with non-normally distributed errors

As pointed out in a recent paper by Amirkhalkhali and Rao (1986) (henceforth referred to as A&R), the usual assumption of normality for the error terms of a regression model isoften untenable. However, when this assumption is dropped, it may be difficult to characterize parameter estimates for the model. For example, A&R (p. 189) state that “if the regression errors are non-normal, we are not even sure of their [e.g., the generalized least squares parameter estimates1] asymptotic properties.” A partial answer, however, is given by Spall and Wall (1984), which presents an asymptotic distribution theory for Kalman filter estimates for cases where the random terms of the state space model are not necessarily Gaussian. Certain of these asymptotic distribution results are also discussed in Spall (1985) in the context of model validation (diagnostic checking)     

Optimal allocation of time points for the random effects model

In this article the problem of the optimal selection and allocation of time points in repeated measures experiments is considered. D‐ optimal designs for linear regression models with a random intercept and first order auto‐regressive serial correlations are computed numerically and compared with designs having equally spaced time points. When the order of the polynomial is known and the serial correlations are not too small, the comparison shows that for any fixed number of repeated measures, a design with equally spaced time points is almost as efficient as the D‐ optimal design. When, however, there is no prior knowledge about the order of the underlying polynomial, the best choice in terms of efficiency is a D‐ optimal design for the highest possible relevant order of the polynomial. A design with equally‐spaced time points is the second best choice     

Gamma shared frailty model based on reversed hazard rate

Abstract

Frailty models are used in survival analysis to account for unobserved heterogeneity in individual risks to disease and death. To analyze bivariate data on related survival times (e.g., matched pairs experiments, twin, or family data), shared frailty models were suggested. Shared frailty models are frequently used to model heterogeneity in survival analysis. The most common shared frailty model is a model in which hazard function is a product of random factor(frailty) and baseline hazard function which is common to all individuals. There are certain assumptions about the baseline distribution and distribution of frailty. In this paper, we introduce shared gamma frailty models with reversed hazard rate. We introduce Bayesian estimation procedure using Markov Chain Monte Carlo (MCMC) technique to estimate the parameters involved in the model. We present a simulation study to compare the true values of the parameters with the estimated values. Also, we apply the proposed model to the Australian twin data set.     

ML and Bayes estimation in a two-phase tandem queue with a second optional service and random feedback

ABSTRACT

In this article, we consider a two-phase tandem queueing model with a second optional service and random feedback. The first phase of service is essential for all customers and after the completion of the first phase of service, any customer receives the second phase of service with probability α, feedback to the tail of the first queue with probability β if the service is not successful and leaves the system with probability 1 ? α ? β. In this model, our main purpose is to estimate the parameters of the model, traffic intensity, and mean system size, in the steady state, via maximum likelihood and Bayesian methods. Furthermore, we find asymptotic confidence intervals for mean system size. Finally, by a simulation study, we compute the confidence levels and mean length for asymptotic confidence intervals of mean system size with a nominal level 0.95.