Sexes and statistics

Arthur Geissler's data for the distribution of the sexes in families with eight children, published in 1889, became famous through its use by R. A. Fisher in Statistical Methods for Research Workers in 1925 as an example of the binomial distribution. Geissler compiled data from Saxony for the period 1876-1885 for all family sizes. How did Fisher obtain the figures for his example? And why did he change the sixth significant figure of his value for the variance in his fourth edition of 1932?     

官方统计之我见

 随着国家教委本科专业目录的出台,中国社会经济统计学界反响很大。振动之余,平下心来。还是有许多东西值得认真反思的。这里之所以用了反思,意在从主观入手,剖析自我。     

Beer and statistics

Occasionally one meets a figure whose memories are of a different era. Stella Cunliffe was president of the Royal Statistical Society from 1975 to 1977. She was, as it happens, the first woman President—the Society has had just one other in the 30 years since then, which might seem on statistical grounds an under-representation. Julian Champkin interviewed her.     

Distribution of concomitants of order statistics and their order statistics

For a random sample of size n$n$ from an absolutely continuous random vector (X,Y)$(X,Y)$, let _Yi:n$Y_{i:n}$ be i$i$th Y$Y$-order statistic and _Y[j:n]$Y_{[j:n]}$ be the Y$Y$-concomitant of _Xj:n$X_{j:n}$. We determine the joint pdf of _Yi:n$Y_{i:n}$ and _Y[j:n]$Y_{[j:n]}$ for all i,j=1$i,j=1$ to n$n$, and establish some symmetry properties of the joint distribution for symmetric populations. We discuss the uses of the joint distribution in the computation of moments and probabilities of various ranks for _Y[j:n]$Y_{[j:n]}$. We also show how our results can be used to determine the expected cost of mismatch in broken bivariate samples and approximate the first two moments of the ratios of linear functions of _Yi:n$Y_{i:n}$ and _Y[j:n]$Y_{[j:n]}$. For the bivariate normal case, we compute the expectations of the product of _Yi:n$Y_{i:n}$ and _Y[i:n]$Y_{[i:n]}$ for n=2$n=2$ to 8 for selected values of the correlation coefficient and illustrate their uses.     

Outliers and order statistics

Outliers are to be found among the extremes of a data set. Extremes are examples of order statistics. It is thus relevant to ask to what extent the statistical methods (and probabilistic properties) of outliers and of order statistics coincide and depend on each other. Whilst clear overlap is identifiable, aims and procedures are often quite distinct and each topic plays its own important role in the panoply of statistical principles and methodology.     

United statistics,confidence quantiles,Bayesian statistics

A survey of research by Emanuel Parzen on how quantile functions provide elegant and applicable formulas that unify many statistical methods, especially frequentist and Bayesian confidence intervals and prediction distributions. Section 0: In honor of Ted Anderson's 90th birthday; Section 1: Quantile functions, endpoints of prediction intervals; Section 2: Extreme value limit distributions; Sections 3, 4: Confidence and prediction endpoint function: Uniform(0,θ)$(0,\theta )$, exponential; Sections: 5, 6: Confidence quantile and Bayesian inference normal parameters μ$\mu$, σ$\sigma$; Section 7: Two independent samples confidence quantiles; Section 8: Confidence quantiles for proportions, Wilson's formula. We propose ways that Bayesians and frequentists can be friends!     

Appealing statistics

In the case of Regina versus Adams [1996], DNA evidence seemed to suggest that there was a 1 in 200 million chance that an innocent person would match the DNA found at the crime scene. Peter Donnelly explains how he subsequently became involved in the case and found himself trying to explain Bayes's Theorem to judge and jury.     

Some invariance principles for mized rank statistics and induced order statistics and some application

The structural affinity of mixed rank statistics and linear combinations of functions of concomitants of order statistics (or induced order statistics) is examined here. Some weal as well as strong invariance principles for these statistics are studied. A variety of models (depend on the nature of stochastic dependence of the two variates) is considered and the regularity conditions are tailored for these diverse situations. Some possible applications of these results in some problems of sequential (statistical) inference are also considered.     

The synoptic problem and statistics

In New Testament studies, the gospels of Matthew, Mark and Luke are known as the synoptic gospels. They contain much common material, and this is particularly clear when their texts are laid out side by side. The gospel of John has a very different style, and there is not such a close correspondence between it and the synoptic gospels. Andris Abakuks focuses on the synoptic problem , hypotheses that attempt to explain the relationships between the synoptic gospels.     

Medical laboratory diagnostics and statistics

We review the statistical contributions to the development and production of laboratory diagnostic assays. The tasks and facets of the role of a statistician in diagnostic industry are discussed.     

Order statistics and test duration

There are two principal issues in statistical planning. One is the accuracy/reliability of statistical inference and the other is the length of test time needed to complete the designed experiment. With regard to the latter, various test schemes have been proposed and applied in statistical literature. These schemes, among others, include type-I censoring, the usual type-II censoring, and progressively type-II censoring. To implement any of these experiments it is necessary that the capacity of the test facility is large enough so that all the items can be tested simultaneously. If, however, instead of having one facility with large capacity there are several facilities with relatively smaller capacities, a differently designed experiment would be necessary. This paper studies and compares elapsed test times and total elapsed test times corresponding to different statistical plans. The results obtained here are useful for performing an experiment that has shorter test time in a certain sense.