Relationships among moments of order statistics in samples from two related outlier models and some applications

Balakrishnan (1987a) has recently shown that the moments of order statistics in samples drawn from a continuous population with pdf f(x) symmetric about zero comprising a single outlier with pdf g(x) also symmetric about zero can be expressed in terms of the moments of order statistics in samples drawn from the population obtained by folding the pdf f(x) at zero and the moments of order statistics in samples drawn from the population obtained by folding the pdf f(x) at zero comprising a single outlier with pdf obtained by folding g(x) at zero. The cumulative round off error involved in the numerical evaluation of the moments of order statistics from the symmetric outlier model, using a table of the moments of order statistics from the folded population and the moments of order statistics from the folded outlier model, has also been studied by Balakrishnan (1987a) and shown to be not serious. Making use of these results we study here the robustness of some estimators of th location and scale parameters of a double exponential distribution.     

Generalized order statistics from two parameter uniform distribution

In this paper some distributional properties of the generalized order statistics from uniform distribution are given. The minimum variance linear unbiased as well best ( in the sense of minimum mean squared error) invariant estimators of the parameters of the two parameter uniform distribution based on the first m generalized order statistics are presented.     

Relative Commodity Prices and Cointegration

The Prebisch–Singer hypothesis of a secular decline in the relative price of primary commodities is reassessed, on the basis of recently available time series data, for 1900–1986. Special attention is given to adequate dynamic modeling of price fluctuations. Primary and manufactured-goods prices are found to be cointegrated. The hypothesis of stationarity for the long-run relative-price movements cannot be rejected. The empirical evidence does not support the Prebisch–Singer hypothesis.     

Use of Dummy Variables in Testing for Equality between Sets of Coefficients in Two Linear Regressions: A Note

Elementary inductive proofs are presented for the binomial approximation to the hypergeometric distribution, the density of an order statistic, and the distribution of when X ₁, ···, X _n are a sample from N (μ, 1).     

The Use of Switching Point and Protection Levels to Improve Revenue Performance in Order‐Driven Production Systems

In a multiproduct order‐driven production system, an organization has to decide how to selectively accept orders and allocate capacity to these orders so as to maximize total profit (TP). In this article, we incorporate the novel concept of switching point in developing three capacity‐allocation with switching point heuristics (CASP_a‐c). Our analysis indicates that all three CASP heuristics outperform the first‐come‐first‐served model and Barut and Sridharan's dynamic capacity‐allocation process (DCAP) model. The best model, CASP_b, has an 8% and 6% average TP improvement over DCAP using the split lot and whole lot policies, respectively. In addition, CASP_b performs particularly well under operating conditions of tight capacity and large price differences between product classes. The introduction of a switching point, which has not been found in previous capacity‐allocation heuristics, provides for a better balance between forward and backward allocation of available capacity and plays a significant role in improving TP.     

Shop Floor Control When Tacit Worker Knowledge is Important

We investigate a shop where the workers and supervisors have tacit knowledge of how to operate efficiently and where efficiency is important to providing capacity to meet demand. This tacit knowledge includes setup dependencies between products as well as which worker or machine is best suited for a particular product. We discuss a real‐world shop where this is the case. Management expects workers and supervisors to use their knowledge to schedule efficiently by monitoring their performance based on standards. The question that we explore is how management should control for due date performance in light of the discretion given to the workers and supervisors to sequence jobs on the basis of efficiency. We explore management control of due date performance through the use of order review and release (ORR) and management expediting. We find that although ORR is quite effective at reducing work‐in‐process (WIP) inventories, it may foster very late deliveries in a shop such as this. In fact, under such conditions, deftly executed expediting with no ORR at all can be far more effective at supporting all deliveries. Even improving ORR into a hybrid by actively updating path efficiencies (observed from supervisor/worker scheduling) did not support a change to this conclusion. Conversely, when conditions are created where tacit knowledge plays a reduced role or utilization is decreased, ORR delivers in a timely manner. The interaction between utilization, WIP levels, and worker knowledge all help dictate the appropriate control methodology.     

Ordered partially ordered judgment subset sampling with applications to parametric inference

ABSTRACT

In this paper, we use the idea of order statistics from independent and non-identically distributed random variables to propose ordered partially ordered judgment subset sampling (OPOJSS) and then develop optimal linear parametric inferences. The best linear unbiased and invariant estimators of the location and scale parameters of a location-scale family are developed based on OPOJSS. It is shown that, despite the presence or absence of ranking errors, the proposed estimators with OPOJSS are uniformly better than the existing estimators with simple random sampling (SRS), ranked set sampling (RSS), ordered RSS (ORSS) and partially ordered judgment subset sampling (POJSS). Moreover, we also derive the best linear unbiased estimators (BLUEs) of the unknown parameters of the simple linear regression model with replicated observations using POJSS and OPOJSS. It is found that the BLUEs with OPOJSS are more precise than the BLUEs based on SRS, RSS, ORSS and POJSS.     

Approximate maximum likelihood estimation of the mean and standard deviation of the normal distribution based on type ii censored samples

It is known that the maximum likelihood methods does not provide explicit estimators for the mean and standard deviation of the normal distribution based on Type II censored samples. In this paper we present a simple method of deriving explicit estimators by approximating the likelihood equations appropriately. We obtain the variances and covariance of these estimators. We also show that these estimators are almost as eficient as the maximum likelihood (ML) estimators and just as eficient as the best linear unbiased (BLU), and the modified maximum likelihood (MML) estimators. Finally, we illustrate this method of estimation by applying it to Gupta's and Darwin's data.