Model Assisted Statistics and Applications

This paper is analyses one of the closed multiple classes queueing networks model by using the discrete review policies. The size of the batches are selected in the network according to discrete positive Poisson distribution and are served according to Exponential distribution. Our aim is to obtain model performance measures when the number of jobs in the system is fixed, the generating parameter of service times changes and also when the generating parameter of service times is fixed, The number ofjobs in the system changes. Finally, We calculate the efficiency measures of the network by using discrete-review policy results through an example.

In this paper, we have suggested a family of estimators π ˆ W for estimating π, the proportion of population having sensitive category, under unrelated question randomized response model. It is shown that the suggested class of estimators π ˆ W of π is more efficient than Mangat et al.’s [8] estimator π ˆ 1 . Since π ˆ W bases on the unknown scalar W, it has little practical utility. By replacing W in π ˆ W by its various estimated values, tww estimators π ˆ W ( i ) , i = 1 , 2 , have been suggested for use in practice. Exact efficiency of π ˆ W ( i ) have been worked out numerically.

Suppose a finite graph containing several vertices, each connected with single or multiple edges. This constitutes a graph population of vertices and edges for example, the population like a tree having a sub-graph in the form of spanning tree. The paper contains mixture of the graph structure and sampling procedure together by virtue of mean-edge estimation of spanning tree using the remaining edges of graph as an auxiliary source of information. A new sampling procedure (node sampling) is derived for this purpose and estimation strategy is proposed to obtain this goal. An optimal sub-class of estimators is obtained. Mathematical conditions for minimum bias and optimum mean squared error are derived and theoretical results are numerically supported with the help of an example of graph population. Almost all the sample estimates of mean-edge length of spanning tree are found within the confidence limits.

Relations between traditional statistical and recently emerging sociophysics paradigms in the social sciences are considered. Similarities and differences between them are analyzed, resulting in a list of the qualitative differences to modeling approaches of reality. Historical review of sociophysics ideas provided, which shows that sociophysics has old and deep, yet often forgotten traces in social and systemic heritage. Importance of complimentary development of two directions in social field is emphasized. Mediaphysics, a branch of sociophysics proposed by the authors, is briefly described as a possible way to use advantages of these two approaches in an organic integrity. It applies general physical models to usual statistical data sets of mass phenomena, which makes it usable for a very wide class of problems, unlike typical physical models, oriented on specific systems. The keystone of the proposed approach is an analysis of population distributions between several alternatives (brands, political affiliations, or opinions) under the influence of internal and external fields.

In this paper we have investigated some classes of shrinkage estimators for estimating dispersion parameter σ in p-dimensional analogue of the probable error of a single variate. The need to study this parameter arises due to its importance in target analysis problems to estimate Circular Probable Error (CPE) and Spherical Probable Error (SPE). It is assumed that the prior information or guessed value of the parameter σ say σ 0 is available from the past experiences. The properties of the developed shrinkage estimators have been studied when center of impact is known and when it is unknown by using appropriate numerical integration method (10-point Gauss-Laguerre integration method). Simulation studies confirm the high efficiency of the developed classes of shrunken estimators when compared with the usual maximum likelihood estimators (MLE), unbiased estimators and minimum mean squared error (MMSE) estimators.