Why Frequency is Not Well Defined for Engineering Systems with Nonexponential Failure Times

Dr. Yellman proposes to define frequency as “a time‐rate of events of a specified type over a particular time interval.” We review why no definition of frequency, including this one, can satisfy both of two conditions: (1) the definition should agree with the ordinary meaning of frequency, such as that less frequent events are less likely to occur than more frequent events, over any particular time interval for which the frequencies of both are defined; and (2) the definition should be applicable not only to exponentially distributed times between (or until) events, but also to some nonexponential (e.g., uniformly distributed) times. We make the simple point that no definition can satisfy (1) and (2) by showing that any definition that determines which of any two uniformly distributed times has the higher “frequency” (or that determines that they have the same “frequency,” if neither is higher) must assign a higher frequency number to the distribution with the lower probability of occurrence over some time intervals. Dr. Yellman's proposed phrase, “time‐rate of events … over a particular time interval” is profoundly ambiguous in such cases, as the instantaneous failure rates vary over an infinitely wide range (e.g., from one to infinity), making it unclear which value is denoted by the phrase “time‐rate of events.”     

Wearing corset,losing shape: The euro's effect on trade imbalances

When does trade become a one-way relationship? We study bilateral trade balances for a sample of 18 European countries over the period from 1948 through 2008. We find that, with the introduction of the euro, trade imbalances among euro area members widened considerably, even after allowing for permanent asymmetries in trade competitiveness within pairs of countries or in the overall trade competitiveness of individual countries. This is consistent with indications that pair-wise trade tends to be more balanced when nominal exchange rates are flexible. Intra-euro area imbalances also seem to have become more persistent with the introduction of the euro, some of which is linked to labor market inflexibility. Reviewing the direction of imbalances, we find that bilateral trade surpluses are decreasing in the real exchange rate, decreasing in growth differentials, and increasing in the relative volatility of national business cycles. Finally, countries with relatively higher fiscal deficits and less flexible labor and product markets exhibit systematically lower trade surpluses than others.     

A modified LGB method for detecting significant effects based on a half-normal probability plot

In analyzing data from unreplicated factorial designs, the half-normal probability plot is commonly used to screen for the ‘vital few’ effects. Recently, many formal methods have been proposed to overcome the subjectivity of this plot. Lawson (1998) (hereafter denoted as LGB) suggested a hybrid method based on the half-normal probability plot, which is a blend of Lenth (1989) and Loh (1992) method. The method consists of fitting a simple least squares line to the inliers, which are determined by the Lenth method. The effects exceeding the prediction limits based on the fitted line are candidates for the vital few effects. To improve the accuracy of partitioning the effects into inliers and outliers, we propose a modified LGB method (hereafter denoted as the Mod_LGB method), in which more outliers can be classified by using both the Carling’s modification of the box plot (Carling, 2000) and Lenth method. If no outlier exists or there is a wide range in the inliers as determined by the Lenth method, more outliers can be found by the Carling method. A simulation study is conducted in unreplicated $2^4$ designs with the number of active effects ranging from 1 to 6 to compare the efficiency of the Lenth method, original LGB methods, and the proposed modified version of the LGB method.     

A permutation alternative and other test procedures for spatially correlated data in one-way anova

Research in many disciplines involves data with spatially correlated observations. Spatial dependence violates the independent errors assumption required for techniques such as the standard one-way analysis of variance for a completely randomized design. The testing methodology within the correlated errors approach has not been investigated within a spatial context. For one-way fixed effects analysis of variance, a permutation test and tests associated with the correlated errors approach are investigated through simulation. No single test was superior with respect to both power and size but the standard Wald F test and a simple adjustment to it performed well overall.     

Estimation and goodness-of-fit procedures for Farlie–Gumbel–Morgenstern bivariate copula of order statistics

In this study, we provide the Farlie–Gumbel–Morgenstern bivariate copula of rth and sth order statistics. The main emphasis in this study is on the inference procedure which is based on the maximum pseudo-likelihood estimate for the copula parameter. As for the methodology, goodness-of-fit test statistic for copulas which is based on a Cramér–von Mises functional of the empirical copula process is applied for selecting an appropriate model by bootstrapping. An application of the methodology to simulated data set is also presented.     

India's demand for international reserve and monetary disequilibrium: Reserve adequacy under floating regime

The main aim of this study is to investigate India's demand for international reserve by focusing on the role of national monetary disequilibrium and to present new benchmarks for assessing the adequacy of international reserves. We assessed India's position in terms of reserve adequacy and found that India is well placed and has sufficient stock of international reserves to meet the minimum adequacy requirements. Also, the results reveal that the central bank is holding substantial excess reserves and the related opportunity cost (1.5% of GDP) appears to be quite considerable. Further, the estimates of reserve demand function suggest that scale of foreign trade, uncertainty and profitability considerations play significant role in determining India's long-term reserve demand policies. More importantly, validating the monetary approach to balance of payment, our results show that national monetary disequilibrium does play a crucial role in short-run reserve movements. An excess of money demand (supply) induces an inflow (outflow) of international reserves with an elasticity of 0.56 which also implies that Reserve Bank of India responds to correct the domestic money market disequilibrium; and did not just leave it completely on the mercy of reserve inflows.     

Least squares estimation of varying‐coefficient hazard regression with application to breast cancer dose‐intensity data

To enhance modeling flexibility, the authors propose a nonparametric hazard regression model, for which the ordinary and weighted least squares estimation and inference procedures are studied. The proposed model does not assume any parametric specifications on the covariate effects, which is suitable for exploring the nonlinear interactions between covariates, time and some exposure variable. The authors propose the local ordinary and weighted least squares estimators for the varying‐coefficient functions and establish the corresponding asymptotic normality properties. Simulation studies are conducted to empirically examine the finite‐sample performance of the new methods, and a real data example from a recent breast cancer study is used as an illustration. The Canadian Journal of Statistics 37: 659–674; 2009 © 2009 Statistical Society of Canada     

Percentile Related Bounds and Estimator for the Mean of the Negative Binomial Distribution

Upper and lower bounds are obtained for the mean of the negative binomial distribution. These bounds are simple functions of a percentile determined by the shape parameter. The result is then used to obtain a robust estimate of the mean when the shape parameter is known.