In finite population (equal as well as unequal probability) sampling late Jaroslav Hajek's contributions to the general asymptotics are fundamental. In the last two decades more research work has been accomplished in this area with the basic ideas germinating from Hajek's work. A systematic review of such developments with due emphasis on some martingale formulations is presented here.

The linkage disequilibrium expected in a finite, partially selfing population is analyzed, assuming the infinite allele model. Formulas for the expected sum of squares of the linkage disequilibria and the squared standard linkage disequilibrium are derived from the equilibrium values of sixteen inbreeding coefficients required to describe the behavior of the system. These formulas are identical...

PracTools is an R package with functions that compute sample sizes for various types of finite population sampling designs when totals or means are estimated. One-, two-, and three-stage designs are covered as well as allocations for stratified sampling and probability proportional to size sampling. Sample allocations can be computed that minimize the variance of an estimator subject to a budge...

where j = i and gi(u1, u2) := (μi − γii ui − γij uj) ui. In the above, the given data is as follows: v is an environmental potential, c i ∈ R≥0, ai ∈ R>0 are diffusion coefficients, bi ∈ R are transport coefficients, μi ∈ R≥0 are the intrinsic growth rates, and γii ∈ R≥0 are intra-specific, whereas γij , i = j, ∈ R≥0 are interspecific competition coefficients. In addition to showing well-posedn...

We model evolution according to an asymmetric game as occurring in multiple finite populations, one for each role in the game, and study the effect of subjecting individuals to stochastic strategy mutations. We show that, when these mutations occur sufficiently infrequently, the dynamics over all population states simplify to an ergodic Markov chain over just the pure population states (where e...

Suppose that U is a U-statistic of degree two based on N random observations drawn without replacement from a nite population. For the distribution of a standardized version of U we construct an Edgeworth expansion with remainder O(N ?1) provided that the linear part of the statistic satisses a Cram er type condition.

In [18], Sighesada, Kawasaki and Teramoto presented a system of partial differential equations for modeling spatial segregation of interacting species. Apart from competitive Lotka-Volterra (reaction) and population pressure (cross-diffusion) terms, a convective term modeling the populations attraction to more favorable environmental regions was included. In this article, we study numerically a...

In this paper we have proposed some ratio-type estimators of finite population variance using known values of parameters related to an auxiliary variable such as quartiles with their properties in simple random sampling. The suggested estimators have been compared with the usual unbiased and ratio estimators and the estimators due to [2], [12, 13, 14] and [3]. An empirical study is also carried...

ALOHA is one of the most basic Medium Access Control (MAC) protocols and represents a foundation for other more sophisticated distributed and asynchronous MAC protocols, e.g., CSMA. In this paper, unlike in the traditional work that focused on mean value analysis, we study the distributional properties of packet transmission delays over an ALOHA channel. We discover a new phenomenon showing tha...

Calibration is commonly used in survey sampling to include auxiliary information at the estimation stage. Calibrating the observation weights on the population means (or totals) of the auxiliary variables implicitly assumes on a linear superpopulation regression model. When auxiliary information is available for all units in the population, more complex modeling can be handled by means of model...