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一种通用的不等概率抽样方案
We present a general purpose unequal probability without replacement sampling plan with fixed sample size. In contrast to existing such plans, our scheme keeps the sample size fixed and lets the population units enter the sample one at a time through a carefully designed random mechanism. Consequently, all high-order inclusion probabilities can be easily computed.
一种通用的不等概率抽样方案
We present a general purpose unequal probability without replacement sampling plan with fixed sample size. In contrast to existing such plans, our scheme keeps the sample size fixed and lets the population units enter the sample one at a time through a carefully designed random mechanism. Consequently, all high-order inclusion probabilities can be easily computed.
非参数函数拟合
Summary In this note we consider the problem of fitting a general functional relationship between two variables. We require only that the function to be fitted is, in some sense, “smooth”, and do not assume that it has a known mathematical form involving only a finite number of unknown parameters.
正随机变量的负阶矩
We investigate the problem of finding the expected value of functions of a random variable X of the form f(X) = (X+A)−n where X+A>0 a.s. and n is a non-negative integer. The technique is to successively integrate the probability generating function and is suggested by the well-known result that successive differentiation leads to the positive moments. The technique is applied to the problem of finding E[1/(X+A)] for the binomial and Poisson distributions.