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何时应停止软件测试？AI 解读

We derive an optimal rule for stopping the testing of a module of software prior to release, based on the trade-off between the cost of continued testing and the expected losses due to any bugs that remain in the released code. Our economic assumptions are that testing costs are perfectly predictable, but of arbitrary form f(t), and that the costs of fixing a bug, both during testing and subsequent to release, are known constants. Our stochastic assumptions are as follows:…

基于重叠数据的估计效率界AI 解读

If we have several estimates of the same quantity, based on partially overlapping sets of data, we can contemplate combining them, linearly, to give a single estimate. We give bounds, which depend only on the degrees of overlap but not on the individual variances, for the efficiency of the best linear unbiased combination of these estimates. with and without covariance information, relative to the overall best linear unbiased estimate. In particular, if the sets have no more…

基于重叠数据的估计效率界AI 解读

If we have several estimates of the same quantity, based on partially overlapping sets of data, we can contemplate combining them, linearly, to give a single estimate. We give bounds, which depend only on the degrees of overlap but not on the individual variances, for the efficiency of the best linear unbiased combination of these estimates. with and without covariance information, relative to the overall best linear unbiased estimate. In particular, if the sets have no more…

非线性平滑器的若干理论AI 解读

In recent years J. W. Tukey has introduced several algorithms for nonlinear smoothing of time series, but theoretical development has been slow owing to the extreme difficulty of obtaining analytical results even in the simplest cases. We present here some desiderata for smoothers generally, and give a framework within which some detailed comparisons between different smoothers can be made.

稳定分布随机变量的模拟方法AI 解读

A new algorithm is presented for simulating stable random variables on a digital computer for arbitrary characteristic exponent α(0 < α ≤ 2) and skewness parameter β(-1 ≤ β ≤ 1). The algorithm involves a nonlinear transformation of two independent uniform random variables into one stable random variable. This stable random variable is a continuous function of each of the uniform random variables, and of α and a modified skewness parameter β' throughout their respective…

正态分布的尺度混合AI 解读

Summary This paper presents necessary and sufficient conditions under which a random variable X may be generated as the ratio Z/V where Z and V are independent and Z has a standard normal distribution. This representation is useful in Monte Carlo calculations. It is established that when 1/2V 2 is exponential, X is double exponential; and that when 1/2V has the asymptotic distribution of the Kolmogorov distance statistic, X is logistic.

差异性无回应导致的面板调查系统偏差AI 解读

Panel surveys involve repeated observations made on the same sample of populalation units. In some of these studies systematic biases have appeared; specifically, if Ri is an estimate made from panels appearing in the sample for the i th time, then it has been observed that these estimates sometimes vary systematically with i. It is tempting to interpret these phenomena as being due to conditioning of the panel of respondents. In this article it is shown that these…

差异性无应答导致的面板调查系统偏差AI 解读

Panel surveys involve repeated observations made on the same sample of populalation units. In some of these studies systematic biases have appeared; specifically, if Ri is an estimate made from panels appearing in the sample for the i th time, then it has been observed that these estimates sometimes vary systematically with i. It is tempting to interpret these phenomena as being due to conditioning of the panel of respondents. In this article it is shown that these…

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切比雪夫不等式的推广AI 解读

Summary We may often obtain the lower moments of a sampling distribution when the distribution itself is intractable. Tchebycheff’s celebrated inequalities for the cumulative distribution function are of very little use in practice, being “much too wide”. The present work obtains generalizations of these inequalities by restricting the distribution function to be “smooth” in two senses: firstly, by restricting the number of changes of sign of some derivative, and secondly by…