W. A. Wallis studied vacancies in the US Supreme Court over a 96-year period (1837-1932) and found that the distribution of the number of vacancies per year could be characterized by a Poisson model. This note updates this classic study.

Describes five statistical simulation programs developed at Wichita State University--Coin Flip and Raindrop, which demonstrate the binomial, Poisson, and other related distributions; Optimal Search; QSIM; and RANDEV, a random deviate generation program. Advantages of microcomputers over mainframes and the educational uses of models are noted.…

Presents a probability model of the occurrence of index terms used to derive discrete distributions which are mixtures of Poisson and negative binomial distributions. These distributions give better fits than the simpler Zipf distribution, have the advantage of being more explanatory, and can incorporate a time parameter if necessary. (25…

Frequency, rank, and frequency rank distributions are defined. Extensive discussion on several aspects of frequency rank distributions includes the Poisson process as a means of exploring the stability of ranks; the correlation of frequency rank distributions; and the transfer coefficient, a new measure in frequency rank distribution. (MBR)

This paper describes details of development of the general birth and death process from which we can extract the Poisson process as a special case. This general process is appropriate for a number of courses and units in courses and can enrich the study of mathematics for students as it touches and uses a diverse set of mathematical topics, e.g.,…

Designed to minimize information overload in telecommunications systems, the formal model developed in this paper predicts the usefulness of a message based on the available message features, and may be used to rank messages by expected importance or economic worth. The assumptions of binary and two Poisson independent probabilistic distributions…

Simulation is an effective tool for analyzing probability models as well as for facilitating understanding of concepts in probability and statistics. Unfortunately, implementing a simulation from scratch often requires users to think about programming issues that are not relevant to the simulation itself. We have developed a Python package called…

The secondary school teacher labour market faces many challenges including, escalating teacher wage bill, teacher shortages that occur alongside teacher surpluses, inadequate teacher distribution and inefficient teacher utilization. There is the need therefore to understand the effects of the factors determining demand for secondary school…

This research is motivated by an analysis of reading research data. We are interested in modeling the test outcome of ability to fluently recode letters into sounds of kindergarten children aged between 5 and 7. The data showed excessive zero scores (more than 30% of children) on the test. In this dissertation, we carefully examine the models…

Concept map structure, testing, and scoring methods are discussed and a new scoring methodology is introduced using the breadth and depth of individual concept maps. The scoring method proposed here provides advantages of grading "on a curve" such as the ability to estimate and compare the complexity of different concept maps, the ability to…

We study the identification and consistency of Bayesian semiparametric IRT-type models, where the uncertainty on the abilities' distribution is modeled using a prior distribution on the space of probability measures. We show that for the semiparametric Rasch Poisson counts model, simple restrictions ensure the identification of a general…

The authors propose and test a simple model of the time course of visual identification of briefly presented, mutually confusable single stimuli in pure accuracy tasks. The model implies that during stimulus analysis, tentative categorizations that stimulus i belongs to category j are made at a constant Poisson rate, v(i, j). The analysis is…

A generally-educated individual should have some insight into how decisions are made in the very wide range of fields that employ statistical and probabilistic reasoning. Also, students of introductory probability and statistics are often best motivated by specific applications rather than by theory and mathematical development, because most…

This article presents the Variable Match Index (VM-Index), a new statistic for detecting answer copying. The power of the VM-Index relies on two-dimensional conditioning as well as the structure of the test. The asymptotic distribution of the VM-Index is analyzed by reduction to Poisson trials. A computational study comparing the VM-Index with the…

This thesis consists of two parts. In Chapter 2, we focus on the spatial scan statistics with overdispersion and Chapter 3 is devoted to the randomized permutation test for identifying local patterns of spatial association. The spatial scan statistic has been widely used in spatial disease surveillance and spatial cluster detection. To apply it, a…