On some probability distributions associated with random walks

The probability distribution of the total number of games to ruin in a gambler's ruin random walk with initial position n, the probability distribution of the total size of an epidemic starting with n cases and the probability distribution of the number of customers served during a busy period M/M/1 when the service starts with n waiting customers are identical. All these can be easily obtained by using Lagrangian expansions instead of long combinatorial methods. The binomial, trinomial, quadrinomial and polynomial random walks of a particle have been considered with an absorbing barrier at 0 when the particle starts its walks from a point n, and the pgfs. and the probability distributions of the total number of jumps (trials) before absorption at 0 have been obtained. The values for the mean and variance of such walks have also been given.     

Educating Effective Social Workers for a Changing Society: Social Policy

The author examines how social policy analysis can be taught so that it is change-related rather than past-oriented. This is done by utilizing a scheme including the concepts of adequacy, effectiveness, and efficiency, which can be applied to both existing and new programs. Subconcepts are utilized to incorporate current concerns, including racial-ethnic aspects, and the analytical framework is linked to the decision-making process.     

Facilitating the Transition from Student to Social Worker: Challenges of the Younger Student

Abstract

The transition from student to social worker is a process which social work educators cannot control but can facilitate. Through classroom and field instruction faculty assumer responsibility of preparing students' professional knowledge, skills, and values; however, our responsibilities should extend beyond curriculum delivery. Drawing on Schlossberg's (1984) model of transitions, this article discusses two primary factors which affect the younger student in transition—developmental needs and the external environment—and strategies for assisting in the transition through intervention in academic advising and teaching roles.     

The behavior of estimated measures of association in small and moderate sample sizes for 2×3 tables

We consider the distributions of Goodman and Kruskal's G, Kendall's tau-b, and correlation coefficients rho and rho-s for sample sizes 10‘10’40 from 2×3 tables. The results are compared with asymptotic theory. It is found that the convergence of G to its asymptotic normal distribution is much slower than the convergence of the other measures to theirs, and that G is more likely to be significantly biased. However, the variances and biases of all four measures come close to their asymptotic values for quite moderate sample sizes.     

The pitman nearness criterion and its determination

A general method for determining Pitman Nearness is given In the case of univariate estimators. This method is then applied to some estimation problems. The concept of Pitman Nearness is also generalized to the multivariate case. The James-Stein estimators are used to illustrate the multivariate comparison.     

Passenger Rail Security,Planning, and Resilience: Application of Network,Plume, and Economic Simulation Models as Decision Support Tools

We built three simulation models that can assist rail transit planners and operators to evaluate high and low probability rail‐centered hazard events that could lead to serious consequences for rail‐centered networks and their surrounding regions. Our key objective is to provide these models to users who, through planning with these models, can prevent events or more effectively react to them. The first of the three models is an industrial systems simulation tool that closely replicates rail passenger traffic flows between New York Penn Station and Trenton, New Jersey. Second, we built and used a line source plume model to trace chemical plumes released by a slow‐moving freight train that could impact rail passengers, as well as people in surrounding areas. Third, we crafted an economic simulation model that estimates the regional economic consequences of a variety of rail‐related hazard events through the year 2020. Each model can work independently of the others. However, used together they help provide a coherent story about what could happen and set the stage for planning that should make rail‐centered transport systems more resistant and resilient to hazard events. We highlight the limitations and opportunities presented by using these models individually or in sequence.     

Chain ratio type estimator for ratio of two population m3ans using auxiliary characters

In this paper we have proposed chain ratio type estimators for ratio of two population means using two auxiliary characters. The expressions for bias and mean square error of these estimators have been derived. A comparison of the proposed estimator with that of double sampling estimator has been made in terms of mean square error. An emperical study has also been made.     

On the total sojourn time of particles in semi-markov compartmental system with branching particles

We consider a semi-Markov compartroental system with branching particles, Me study the total sojourn time of all the particles and obtain the asymptotic behaviour of its mean. We also discuss some special systems.     

Maximum likelihood estimation for the generalized poisson distribution

The generalized Poisson distribution;containing two

parameters and studied by many researchers; describes the distribution of busy periods under a queueing system and has very interesting properties; The probabilities for successive classes depend upon the previous occurrences; The problem of admissible maximum likelihood estimators for for the parameters Is discussed and a necessary and sufficient condition is derived for which unique admissible maximum likelihood estimators exist; The first; order terms in the biases; variances and the covariance of these maximum likelihood estimators are obtained.