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As increasingly complex algorithms are implemented on statistical software, benchmarks serve as an important means to identify and correct potential aws that may lead to inaccurate results in real applications In 2 we explain why the computer algorithms on which statistical software are built contain unavoidable numerical inaccuracies Unfortunately, comprehensively testing statistical packages for all numerical inaccuracies is practically impossible given the amount of time that is required to investigate all algorithms In lieu of an exhaustive analysis of a statistical program, benchmarks serve as a basis for assessing their degree of numerical accuracy Benchmarks are problems models and data with known answers that can be compared to the estimates produced by statistical packages Here we describe three sets of benchmarks, each corresponding roughly to a source of inaccuracy as described in 2: oating point approximation error, inaccuracies in distribution functions, and inaccuracies in pseudo-random number generation.

iteration should be traceable back to both the requirements and the design. If the requirements or design changed, appropriate modi cations should be embodied in the code immediately to minimize the amount of necessary rework.

Advanced reporting and visualization tools add value by enabling the end user to view the analysis results in highly useful and diverse ways. This includes the use of various types of charts, graphs, color codes, alerts, or multidimensional visual constructs and images that the end user can manipulate directly (rotate, pivot, reshape, resize, and so on). Data marts, advanced analysis tools (including software-based analysis packages, OLAP servers, and data mining packages), and reporting and visualization tools collectively represent the final refinement step in the ISC, in which strategic, dimensional business information is effectively transformed into business knowledge, insight, or vision.

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In addition, we benchmark an overlooked source of inaccuracy: basic processes of data input and export 321 NIST Statistical Reference Datasets The Statistical Engineering and Mathematical and Computational Sciences Divisions of the National Institute of Standards and Technology s (NIST) Information Technology Laboratory maintains a set of benchmark problems called the Statistical Reference Datasets (StRD), which are accompanied by certi ed values for a variety of statistical problems These datasets provide benchmarks for assessing the accuracy of univariate descriptive statistics, linear regression, analysis of variance, and nonlinear regression (Rogers et al 2000) The collection includes both generated and experimental data of varying levels of dif culty and incorporate the best examples of previous benchmarks, such as Simon and LeSage (1988) and Longley (1967).

If you keep these written equipment requirements readily available, it becomes a great deal easier to reject unwanted donations without hurt feelings. If potential donors have lost track of the printed materials that came with their computer, you can explain to them that it is easy to click on System Information on their Windows menu.They might wish to print out the information displayed and bring the printout to you rather than the computer.

Since the release of the StRD, numerous reviewers have used them to assess the accuracy of software packages, and vendors of statistical software have begun to publish the test results themselves To gauge the reliability of a statistical package using the StRD, one loads the data into a program, runs the speci ed analysis, and compares the results to the certi ed values Good performance on the StRD provides evidence that a software package is reliable for tested algorithms, but of course, provides no evidence for untested algorithms For each tested algorithm, the StRD contain multiple problems designed to challenge various aspects of the algorithm The benchmark problems are named and assigned three levels of dif culty: low, average, and high.

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Advantages of current limitation The use of current-limiting circuit-breakers provides numerous advantages: better network protection: limiting circuit-breakers greatly reduce all the harmful effects of short-circuit currents in an installation; reduction of thermal effects: a smaller heat rise in the conductors leading to increased cable life; reduction of mechanical effects: electrodynamic forces of repulsion (see section 5.2) are reduced, so there is less risk of elements being deformed or ruptured, especially the electrical contacts; reduction of electromagnetic effects: less influence on measuring instruments located near an electrical circuit. These circuit-breakers contribute to improving the protection of: cables; prefabricated trunking; electrical switchgear. This means that they slow down installation aging. Example For a prospective short-circuit current of 150 kA r.m.s., a circuit-breaker limits the peak current to less than 10% of the value calculated and the thermal effects (proportional to the square of the current; see section 5.1) to less than 1% of the calculated effects. 8.2. MV circuit-breakers (according to standard IEC 62271-100) The rated short-circuit breaking capacity This is the highest short-circuit current that the circuit-breaker is able to interrupt. The rated short-circuit breaking capacity is characterized by two values (see IEC 62271-100, section 4.101): the r.m.s. value of its AC component (see section 4.1), termed rated shortcircuit breaking capacity for short; the DC component percentage (see section 4.1). The percentage of DC component is the ratio between the DC component and the AC component during the minimum opening time of the circuit-breaker,

Straightforward calculations show that this is maximized for c D 1=4, and takes the value 5=12 (D 0:4167). Case 4. In the English auction with a reserve price p, there is no sale with probability p2 . The revenue is p with probability 2 p.1 p/. If minfv1 ; v2 g > p, then the sale price is minfv1 ; v2 g. The expected revenue is 2 p2 .1 p/ C 1 C 2 p .1 p/2 3 3 This is maximized by p D 1=2 and the expected revenue is again 5=12, exactly the same as in case 3.

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