Abstract Abstract Consider the problem of estimating the mean by using a random sample from a normal population. Let denote the sample mean and consider the estimator that assumes the value zero when and the value when . This is called a preliminary test estimator. For most of the usual loss functions it is inadmissible. In this article we show that for some loss functions, which include a complexity cost, the estimator is admissible. The results are related to Cohen's work on hybrid estimation and hypothesis-testing problems. Key Words: AdmissibilityPreliminary testComplexity costNormal mean
It is known that all the proportional reversed hazard (PRH) processes can be de?rived by a marginal transformation applied to a power function distribution (PFD) process. Kundu [8] investigated PRH processes that can be viewed as being ob?tained by marginal transformations applied to a particular PFD process that will be described and investigated and will be called a Kundu process. In the present note, in addition to studying the Kundu process, we introduce a new PFD process having Markovian and stationarity properties. We discuss distributional features of such processes, explore inferential aspects and include an example of applications of the PFD processes to real-life data.
Control charts are effective tools for monitoring both manufacturing processes and service processes. Much service data comes from a process with variables having non-normal or unknown distributions. The commonly used Shewhart variable control charts which depend heavily on the normality assumption should not be applied here. Hence, an alternative is desired to handle these types of process data. In this paper, we propose a new Variance Chart based on a simple statistic to monitor process variance shifts. The sampling properties of the new monitoring statistic are explored. A numerical example of service times from a bank service system with a right skewed distribution is used to illustrate the proposed Variance Chart. A comparison with two existing charts is also performed. The Variance Chart showed better ability than those two charts in detecting shifts in the process variance.
Control charts are effective tools for signal detection in both manufacturing processes and service processes. Much of the data in service industries comes from processes having nonnormal or unknown distributions. The commonly used Shewhart variable control charts, which depend heavily on the normality assumption, are not appropriately used here. In this paper, we propose a new asymmetric EWMA variance chart (EWMA-AV chart) and an asymmetric EWMA mean chart (EWMA-AM chart) based on two simple statistics to monitor process variance and mean shifts simultaneously. Further, we explore the sampling properties of the new monitoring statistics and calculate the average run lengths when using both the EWMA-AV chart and the EWMA-AM chart. The performance of the EWMA-AV and EWMA-AM charts and that of some existing variance and mean charts are compared. A numerical example involving nonnormal service times from the service system of a bank branch in Taiwan is used to illustrate the applications of the EWMA-AV and EWMA-AM charts and to compare them with the existing variance (or standard deviation) and mean charts. The proposed EWMA-AV chart and EWMA-AM charts show superior detection performance compared to the existing variance and mean charts. The EWMA-AV chart and EWMA-AM chart are thus recommended.
Abstract This article considers a class of multivariate (dependent) variables that includes those that are obtained as scale mixtures of elliptically symmetric distributions. We provide a simple, intuitive proof that the ratio of two such variables has a general Cauchy distribution. This result extends the results of DeSilva concerning properties of a certain class of dependent multivariate symmetric stable distributions.
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