A note on Bayesian estimation of traffic intensity in single-server Markovian queues

ABSTRACT

In queuing theory, a major interest of researchers is studying the behavior and formation process and analyzing the performance characteristics of queues, particularly the traffic intensity, which is defined as the ratio between the arrival rate and the service rate. How these parameters can be estimated using some statistical inferential method is the mathematical problem treated here. This article aims to obtain better Bayesian estimates for the traffic intensity of M/M/1 queues, which, in Kendall notation, stand for Markovian single-server infinity queues. The Jeffreys prior is proposed to obtain the posterior and predictive distributions of some parameters of interest. Samples are obtained through simulation and some performance characteristics are analyzed. It is observed from the Bayes factor that Jeffreys prior is competitive, among informative and non-informative prior distributions, and presents the best performance in many of the cases tested.     

Exponentiality test based on Renyi distance between equilibrium distributions

ABSTRACT

On the basis of Csiszar's φ-divergence discrimination information, we propose a measure of discrepancy between equilibriums associated with two distributions. Proving that a distribution can be characterized by associated equilibrium distribution, a Renyi distance of the equilibrium distributions is constructed that made us to propose an EDF-based goodness-of-fit test for exponential distribution. For comparing the performance of the proposed test, some well-known EDF-based tests and some entropy-based tests are considered. Based on the simulation results, the proposed test has better powers than those of competing entropy-based tests for the alternatives with decreasing hazard rate function. The use of the proposed test is evaluated in an illustrative example.     

Estimation for the bivariate normal correlation coefficient using asymptotic expansions

Harley (1954) gave asymptotic expansions for the distributio function and for percentiles of the distribution of the bivariate normal sample correlation coefficient. To the stated order of approximation these expansions were incomplete in that contributions from some higher cumulants were not taken into account. In this article the completed expansions are given together with an asymptotic expansion yielding approximate confidence limits for the population correlation coefficient. Numerical comparisons indicate that asymptotic expansions are superior to other suggested approximate methods     

A network algorithm for the exact treatment of the 2×k contingency table

A common statistical problem encountered in biomedical research is to test the hypothesis that the parameters of k binomial populations are all equal. An exact test of significance of this hypothesis is possible in principle, the appropriate null distribution being a normalized product of k binomial coefficients. However, the problem of computing the tail area of this distribution can be formidable since it requires the enumeration of all sets of k binomial coefficients whose product is less than a given constant. Existing algorithms, all of which rely on explicit enumeration to generate feasible binomial coefficients     

A note on the accuracy of fisher's approximation to the large sample variance of an intraclass correlationa

The adequacy of Fisher's approximation to the large sample variance of an intraclass correlation is investigated in the context of family studies. It is found that the approximation is highly accurate in samples of moderately large size (≧ 30 families), and can also be used for significance-testing under a broad range of circumstances. The exact sampling of distribution of the intraclass correlation coefficient is also derived.     

Comparing several experimental groups with a control in the multivariate case

This paper presents a multivariate extension of Dunnett's test for comparing simultaneously k treatment group means with a single control group mean. A test based on Hotelling T²statistics is presented and approximate critical values are evaluated for the case of equal numbers of observations in each group, for the .05 and .01 levels of significance, for 1 to 5 variates, for 1 to 10 treatment groups, and for varying degrees of freedom. The accuracy of the procedure for generating approximate critical values is assessed via simulation studies conducted for selected cases and an example is presented using real data.     

Modified weighted squared error estimation procedures with special emphasis on the stable laws

Two families of parameter estimation procedures for the stable laws based on a variant of the characteristic function are provided. The methodology which produces viable computational procedures for the stable laws is generally applicable to other families of distributions across a variety of settings. Both families of procedures may be described as a modified weighted chi-squared minimization procedure, and both explicitly take account of constraints on the parameter space. Influence func-tions for and efficiencies of the estimators are given. If x₁, x₂, …x_n random sample from an unknown distribution F , a method for determining the stable law to which F is attracted is developed. Procedures for regression and autoregres-sion with stable error structure are provided. A number of examples are given.     

An improved graphical procedure for multivariate-quality control

In an earlier article (Kulkarni and Paranjape 1984) we proposed a procedure based on Andrews' function plot technique for the quality control of multivariate process. It was shown that this procedure may lead to an erroneous conclusions regarding the status of the process. This article presents an improved method which avoids the above drawback. A heuristic justification is provided to show that the new method is free from the error. Simulation studies are carried out to support the claim. An example is included to illustrate the use of the new technique.     

On asymptotic distribution of the test statistic for the mean of the non-isotropic principal component

In this paper, the authors derived the large sample distribution of the t statistic based upon the observations on the first principal component instead of the original variables. It is shown that the above statistic is distributed asymptotically as Student's t distribution.     

A comparison of some conditional and unconditional exact tests for 2x2 contingency tables

In 1935, R.A. Fisher published his well-known “exact” test for 2x2 contingency tables. This test is based on the conditional distribution of a cell entry when the rows and columns marginal totals are held fixed. Tocher (1950) and Lehmann (1959) showed that Fisher s test, when supplemented by randomization, is uniformly most powerful among all the unbiased tests UMPU). However, since all the practical tests for 2x2 tables are nonrandomized - and therefore biased the UMPU test is not necessarily more powerful than other tests of the same or lower size. Inthis work, the two-sided Fisher exact test and the UMPU test are compared with six nonrandomized unconditional exact tests with respect to their power. In both the two-binomial and double dichotomy models, the UMPU test is often less powerful than some of the unconditional tests of the same (or even lower) size. Thus, the assertion that the Tocher-Lehmann modification of Fisher's conditional test is the optimal test for 2x2 tables is unjustified.