Optimal component test plans for a parallel system based on Type-II censoring

Consider a parallel system with n independent components. Assume that the lifetime of the jth component follows an exponential distribution with a constant but unknown parameter λ_j, 1≤j≤n. We test r_j components of type-j for failure and compute the total time T_j of r_j failures for the jth component. Based on T=(T₁,T₂,…,T_n) and r=(r₁,r₂,…,r_n), we derive optimal reliability test plans which ensure the usual probability requirements on system reliability. Further, we solve the associated nonlinear integer programming problem by a simple enumeration of integers over the feasible range. An algorithm is developed to obtain integer solutions with minimum cost. Finally, some examples have been discussed for various levels of producer’s and consumer’s risk to illustrate the approach. Our optimal plans lead to considerable savings in costs over the available plans in the literature.     

Bayesian demography 250 years after Bayes

Bayesian statistics offers an alternative to classical (frequentist) statistics. It is distinguished by its use of probability distributions to describe uncertain quantities, which leads to elegant solutions to many difficult statistical problems. Although Bayesian demography, like Bayesian statistics more generally, is around 250?years old, only recently has it begun to flourish. The aim of this paper is to review the achievements of Bayesian demography, address some misconceptions, and make the case for wider use of Bayesian methods in population studies. We focus on three applications: demographic forecasts, limited data, and highly structured or complex models. The key advantages of Bayesian methods are the ability to integrate information from multiple sources and to describe uncertainty coherently. Bayesian methods also allow for including additional (prior) information next to the data sample. As such, Bayesian approaches are complementary to many traditional methods, which can be productively re-expressed in Bayesian terms.     

球面最小范数插值的误差估计

由球面一基本系及半内积空间构成一Hilbert函数空间，对该函数空间上的最小范数插值，给出了一致误差估计．     

CALCULATING THE TRUE COST OF PRIVATE SCHOOL EDUCATION: BASED ON A SURVEY OF SOUTH AUSTRALIAN SCHOOL FEES

The cost of a child's education should not be a mystery to consumers, yet little has been published about the true costs, and it is no simple task for parents to calculate. This paper seeks to fill a gap in the research literature that exists in relation to informing parents and educationalists alike as to the true cost of private school education. The term cost is used in the economic sense as encompassing not only the price paid for the product (school fees) but also the opportunity cost to the family in terms of what they forego in order to finance private schooling. Identifying opportunity cost is a useful means of assessing the impact of factors, other than financial, that are influential in determining whether or not private education is purchased. From a survey of South Australian private schools, we have been able to provide a detailed account of the price variations between the fees charged, as well as identifying a variety of additional ancillary charges. Based on the survey figures, we have projected the amount of money that needs to be taken out of the family budget in order to pay for a child's private schooling. At the time the survey was conducted the cost of private school education across three strata, on average, ranged from $13,400 to $42,246. We calculated that incremental family pretax incomes of between $20,303 and $64,009 would be required to fund this education. The amounts represent an opportunity cost to a family whereby money could be put to alternative uses such as home renovation, an overseas holiday, or a buffer against unexpected life events. We conclude that the outlay is substantial for many families and that greater transparency of all costs is needed for families to make informed financial plans to accommodate the overall cost of education for their children.     

Asymptotic distribution of data-driven smoothers in density and regression estimation under dependence

We consider automatic data-driven density, regression and autoregression estimates, based on any random bandwidth selector h/_T. We show that in a first-order asymptotic approximation they behave as well as the related estimates obtained with the “optimal” bandwidth h_T as long as h_T/h_T → 1 in probability. The results are obtained for dependent observations; some of them are also new for independent observations.     

Product-limit survival functions with correlated survival times

A simple variance estimator for product-limit survival functions is demonstrated for survival times with nested errors. Such data arise whenever survival times are observed within clusters of related observations. Greenwood's formula, which assumes independent observations, is not appropriate in this situation. A robust variance estimator is developed using Taylor series linearized values and the between-cluster variance estimator commonly used in multi-stage sample surveys. A simulation study shows that the between-cluster variance estimator is approximately unbiased and yields confidence intervals that maintain the nominal level for several patterns of correlated survival times. The simulation study also shows that Greenwood's formula underestimates the variance when the survival times are positively correlated within a cluster and yields confidence intervals that are too narrow. Extension to life table methods is also discussed.     

Computationally efficient classes of higher-order kernel functions

Classes of higher-order kernels for estimation of a probability density are constructed by iterating the twicing procedure. Given a kernel K of order l, we build a family of kernels K_m of orders l(m + 1) with the attractive property that their Fourier transforms are simply 1 — {1 —$(.)}^m+1, where ? is the Fourier transform of K. These families of higher-order kernels are well suited when the fast Fourier transform is used to speed up the calculation of the kernel estimate or the least-squares cross-validation procedure for selection of the window width. We also compare the theoretical performance of the optimal polynomial-based kernels with that of the iterative twicing kernels constructed from some popular second-order kernels.     

ON A SHARED ALLELE TEST OF RANDOM MATING

A simple random sample is observed from a population with a large number‘K’ of alleles, to test for random mating. Of n couples, n_ijkl have female genotype ij and male genotype kl (i, j, k, l{1,…, A‘}). The large contingency table is collapsed into three counts, n₀, n₁ and n₂ where n_p is the number of couples with s alleles in common (s = 0,1, 2). The counts are estimated by np?_o where n₀, is the estimated probability of a couple having s alleles in common under the hypothesis of random mating. The usual chi-square goodness of fit statistic X² compares observed (n_s) with expected (np?) over the three categories, s = 0,1,2. An empirical observation has suggested that X² is close to having a chi-square distribution with two degrees of freedom (X) despite a large number of parameters implicitly estimated in _e. This paper gives two theorems which show that x is indeed the approximate distribution of X² for large n and K₁“, provided that no allele type over-dominates the others.     

Counting snowbirds: The importance of and the problems with estimating seasonal populations

Using the example of the seasonal population of ``snowbirds' that spend the winter in Arizona and other Sunbelt states, this paper examines the issues involved with estimating temporary populations. Specifically using the experience of ASU's ongoing research efforts on Arizona snowbirds, the paper discusses some of the problems associated with estimating a seasonal population – in particular: (1) defining the population under study and (2) developing effective procedures to collect information relating to the population. The concluding section emphasizes the growing national importance of temporary populations and the needs of both the public and private sector to have better information on both their size and characteristics.     

Origin dependence, secondary migration, and the indirect estimation of migration flows from population stocks

US census data from 1940 to 2000 are used in this paper to illustrate the importance of origin dependence on migration streams and to examine the effects of such dependence on patterns of interregional migration. These findings are then used to make possible the indirect estimation of migration flows. A method is introduced that uses historical regularities found in the ratios of secondary to primary migration and two consecutive birthplace-specific counts of multiregional population stocks. The results demonstrate how patterns of primary and secondary migration act to shape population redistribution processes.