From the known statistics of fiber-fiber contacts in random fiber networks, an analytic estimate is obtained for the variance of local porosity in random fiber suspensions and evolving filtrate networks. The variance of local porosity, and hence the distribution of projected areal density, seem to depend on fiber geometry only through the cube of mean diameter. Also, the coefficient of variatio...

Abstract: This paper develops some objective priors for certain parameters of the bivariate normal distribution. The parameters considered are the regression coefficient, the generalized variance, and the ratio of the conditional variance of one variable given the other to the marginal variance of the other variable. The criterion used is the asymptotic matching of coverage probabilities of Bay...

This analysis introduces a generalization of the basic statistical concepts of expectation values and variance for non-Euclidean metrics induced by L-norms. The non-Euclidean L means are defined by exploiting the fundamental property of minimizing the L deviations that compose the L variance. These L expectation values embody a generic formal scheme of means characterization. Having the p-norm ...

From the known statistics of fibre-fibre contacts in random fibre networks, an analytic estimate is obtained for the variance of local porosity in random fibre suspensions and evolving filtrate networks. The variance of local porosity, and hence the distribution of projected areal density, seems to depend on fibre geometry only through the cube of mean diameter. Also, the coefficient of variati...

Commutative Jordan algebras are used to express the structure of mixed orthogonal models and to derive complete sufficient statistics. From these statistics, UMVUE, (Uniformly Minimum Variance Unbiased Estimators), are derived for the relevant parameters, first of single models then of several such models. These models may correspond to experiments designed separately so our results may be seen...

The statistics of outbreaks in a model for the propagation of meningococcal disease is analyzed, taking into account the possibility that the population is fragmented into weakly connected patches. It is shown that, depending on the size of the sample studied, the ration between the variance and the average of infected cases can vary from unity (Poisson statistics) to epsilon(-1), where epsilon...

This material is designed to introduces basic concepts and fundamental theory of mathematical statistics. A review of basic concepts will include likelihood functions, sufficient statistics, and exponential family of distributions. Then point estimation will be discussed, including minimum variance unbiased estimates, Cramér-Rao inequality, maximum likelihood estimates and asymptotic theory. To...

We present a class of haplotype-sharing statistics useful for association mapping in case-parent trio data. The framework presented allows derivation of novel tests as well as new simplified variance estimators for previously proposed tests. We give an overview of this framework and apply four such tests to the simulated data of Genetic Analysis Workshop 15. We find that these haplotype-based s...

The following paper represents a further study of topics considered in Statistics 150 and Statistics 254 at the University of North Carolina at Chapel Hill and Statistics 691 at North Carolina State University at Raleigh. Its primary purpose is to investigate the effect of restrictions and redundancies in linear models. An additional topic considered is the effect of a variance-covariance matri...

In the case of two signals with independent pairs of observations (xn; yn) a statistic to estimate the variance of the mutual information estimator has been derived earlier. We present such a statistic for dependent pairs. To derive this statistic it is necessary to avail of a reliable statistic to estimate the variance of the sample mean in case of dependent observations. We derive and discuss...