Online Control Charts for Process Averages Based on Repeated Median Filters

Two types of estimates of process level, namely repeated median estimates (Siegel, 1982 Siegel , A. F. ( 1982 ). Robust regression using repeated medians . Biometrika 69 : 242 – 244 .[Crossref], [Web of Science ®] , [Google Scholar]) and full online estimates (Gather et al., 2006 Gather , U. , Schettlinger , K. , Fried , R. ( 2006 ). Online signal extraction by robust linear regression . Computational Statistics 21 : 33 – 51 .[Crossref], [Web of Science ®] , [Google Scholar]) based on repeated median filters, are used to develop control charts. The distributional properties of the estimates are studied using simulation and these are found to closely follow normal distribution. The repeated median being robust against outliers with asymptotically 50% breakdown value and having small standard deviation is found to be useful as a basis for monitoring process averages. The control charts using repeated median estimates have been recommended for general use.     

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.     

Discrete Linnik Weibull distribution

Abstract

We introduce a new family of distributions using truncated discrete Linnik distribution. This family is a rich family of distributions which includes many important families of distributions such as Marshall–Olkin family of distributions, family of distributions generated through truncated negative binomial distribution, family of distributions generated through truncated discrete Mittag–Leffler distribution etc. Some properties of the new family of distributions are derived. A particular case of the family, a five parameter generalization of Weibull distribution, namely discrete Linnik Weibull distribution is given special attention. This distribution is a generalization of many distributions, such as extended exponentiated Weibull, exponentiated Weibull, Weibull truncated negative binomial, generalized exponential truncated negative binomial, Marshall-Olkin extended Weibull, Marshall–Olkin generalized exponential, exponential truncated negative binomial, Marshall–Olkin exponential and generalized exponential. The shape properties, moments, median, distribution of order statistics, stochastic ordering and stress–strength properties of the new generalized Weibull distribution are derived. The unknown parameters of the distribution are estimated using maximum likelihood method. The discrete Linnik Weibull distribution is fitted to a survival time data set and it is shown that the distribution is more appropriate than other competitive models.     

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 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.     

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.     

A new test for the extreme value distribution

In this paper a test statistic which is a modification of the W statistic for testing the goodness of fit for the two paremeter extreme value (smallest element) distribution is proposed. The test statistic Is obtained as the ratio of two linear estimates of the scale parameter. It Is shown that the suggested statistic is computationally simple and has good power properties. Percentage points of the statistic are obtained by performing Monte Carlo experiments. An example is given to illustrate the test procedure.